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.

To my mind, the overriding rules here are these:

Alternate Form

The creature retains the type and subtype of its original form.

Undead Type

• No Constitution score.

You cannot have an undead that has a Constitution score, so since Alternate Form has you retain your type, you cannot gain a Constitution score. I believe this is “more specific” than the general rule that you gain the target creature’s physical ability scores when using Alternate Form.

You could argue the opposite way, however, that Alternate Form is a more specific case than the general rule that undead do not have a Constitution score. But note that this results in a living (has a Constitution score) undead (retains that type), which to me is a good enough reason to side the other way.

As for using Charisma in place of Constitution, this is a common feature for undead, but not a universal one. In some places, that privilege requires a feat (e.g. Undead Meldshaping in Magic of Incarnum). Depending on your build, I might want to tax you for it; Cha-to-everything is a fairly potent strategy as it is, and undead is a desirable type anyway. Getting to use Charisma for yet more things, and avoiding the “weakness” of the undead type’s lack of Constitution, might be problematic. But if you weren’t already pursuing a Cha-to-everything build, I’d probably give it freely.