Yes.

The actual rules for this are oddly worded, but the notation is pretty simple.

In general, there are two formats for "things that increase your AC." The most common format is the one attached to armor:

[your AC equals] 11 + Dex modifier

or Draconic Resilience:

your AC equals 13 + your Dexterity modifier.

Note that there is no "plus" at the beginning of the formula. These items set your AC to a specific value.

The other format is that used by shields and class features that increase your AC above its base value:

Defensive fighting style:

You gain a +1 bonus to AC.

Or a shield:

Wielding a shield increases your AC by 2.

These are phrased in terms of increasing, rather than setting your AC. They are preceded by the phrase "increases" or a plus sign.

So, it's pretty simple. You get one thing that sets your AC, and any number of things that modify it (except where restricted by other rules, like the rules stating you can only use one shield).

A fighter could very easily have an AC like this:

[15 + Dex Mod] (half-plate) [+2] (shield) [+1] (defensive fighting style)

For a total AC of 18 + Dex Mod.

But he couldn't add a chain shirt to increase his AC, because both that and the half-plate set his AC to a fixed value.

The same applies to Draconic Resilience. You can stack it with a shield, because a shield increases AC. And you can further stack on the Shield spell, giving you a (temporary) total of [13 + Dex Mod] [+2] [+5], or 20 + Dex Mod.

But you can't combine Draconic Resilience with Mage Armor, because both Mage Armor and Draconic Resilience are trying to set your AC to a fixed value.

Some things Draconic Resilience stacks with:

• Shields

• Shield spell

Some things it does not:

• Plate

• Mage Armor spell

• Barbarian Unarmored Defense class feature

RAW

The rules for AC are on page 14 of the Player's Handbook, or page 9 of the Basic Rules.

The relevant part is this:

Without armor or a shield, your character’s AC equals 10 + his or her Dexterity modifier. If your character wears armor, carries a shield, or both, calculate your AC using the rules in chapter 5. Record your AC on your character sheet.

[...]

Some spells and class features give you a different way to calculate your AC. If you have multiple features that give you different ways to calculate your AC, you choose which one to use.

The rules called out above appear to be these:

Wielding a shield increases your Armor Class by 2. You can benefit from only one shield at a time.

If you wear light armor, you add your Dexterity modifier to the base number from your armor type to determine your Armor Class.

(and so on, for each type of armor)

The rules are sloppy here. Technically, they don't give you a calculation for AC when wielding a shield and no armor. And they never explicitly call out what is or is not a "way to calculate your AC."

With that said, we can use examples to build the intent of the designers.

It's pretty clear that you don't have to choose between a shield and plate. It's also pretty clear that a shield shouldn't set your AC to 2.

Finally, it's pretty clear that wearing a chain shirt with half plate shouldn't set your AC to 28 + 2 * Dex modifier (max 2).

It seems obvious then, that a "calculation" is something that sets your AC to a value plus other modifiers.

If something just adds on to (or increases) your AC, you continue to use whichever calculation is most favorable plus the new modifier.

This is the wonder of RPGs, they are flexible. But they are not without their trade-offs here.

Probably not an issue

• Spell DCs
• Spell Attack modifiers

Probable issues

• Physical vs Mental
• Saves
• Skills
• Flavour

Let's break these out.

Physical vs Mental

Casting is generally tied to one of the three Mental stats (Int, Wis, Cha). If you allowed an Eldritch Knight Fighter to make their casting stat Str this would probably cause power issues because you would be letting them "double-down" on their best stats. Likewise for Arcane Tricksters, Paladins, Rangers.

Saves

The game technically has six saves, but Dex, Con & Wis are really the most important saves. If you look at the Save Proficiencies by class, each class only gains proficiency in one of these two saves. They also typically gain proficiency in the save that matches their best stat.

So Sorcerers get proficiency in Cha saves making them really good at Cha saves. Rogues are really good a Dex saves, Clerics are really good at Wis saves, etc. If you make a Wis Sorcerer, they become "pretty good" at Cha saves, but also pretty good at Wis saves.

This definitely changes the nature of the class. You normally don't target a Cleric or Druid with a Wis save because it's probably not going to work. But now it's not so clear. This will affect both PCs and NPC casters.

Skills

Available skills tend to be connected to a character's primary stat. So Clerics get more Wis skills and Wizards get more Int skills. If you switch this around, it really reduces the odds of having someone particularly skilled at one of these disciplines. If the Cleric doesn't have a good Medicine score, then who does? Same for Arcana?

Fortunately, some of these can be made up for with specific Backgrounds, but it does hamper specialization usually connected with the given classes.

Flavour

There is a specific history behind the various casting stats. Int casters had to study, Wis casters are divinely inspired, Cha casters are "naturals". When you switch this stuff around, you're also implying a different world vision than the "classic" D&D.

This is not "bad" per se. But it is significant. Why does a low Int Wizard use a spell book? Are they really going to be book worms if they use Cha to cast? If Sorcerers use Int to cast, but don't need books is there a reason for that? If Clerics use Int to cast, then where does that whole "divine inspiration" thing kick in?

These questions can clearly be reconciled, but they are meaningful. They say something about your game world that is different from say a classic Forgotten Realms world.