My teammate last night had a couple of exotic shards sitting around and tested this. He Ascended two exotic weapons: one fully upgraded and one not. The weapon that wasn't fully upgraded did not have its damage upgrade nodes unlocked automatically after the Ascend, so it looks like you still need to fully upgrade the weapon to maximize its potential. Granted, this test was with Exotic equipment, legendaries may be different.
I think this Ascend feature was less for maxing out incomplete equipment, and more for upgrading maxed out equipment from the pre DLC 1 days. Case in point, I have a Vision of Confluence from the Vault of Glass that was awesome until the first DLC launched with higher damage weapons. With the Ascend feature, this weapon becomes useful again.
The light "level" of your character is an average of your gear's light.
For this reason, at level 34 when everyone only had 170 gear the "cap" was 170. Now, for the same reason, the cap of gear's light level will be the cap of player light level.
I have seen prior that the new Trials of Osiris lighthouse gear will be given out fully maxed at 310. This leads me to believe that 310 is the cap for gear, and by relation 310 would be the light level cap.
As the release was only yesterday, there is obviously going to be more information to come, but for now this is as close as possible.
List of Taken King known gear
Video of several 310 Trials pieces along with other new gear
310 Auto Rifle Doctrine of Passing (Adept)destinyDB "Death is the best teacher"
edit
After playing for some more time, here is the breakdown.
Non raid gear, even blues and legendaries, will only drop with a cap of 300.
In order to reach this pre raid level, it is best to identify your items from the cryptarch one item at a time, ensuring to equip it as you go if it is a higher light level - this will affect future light levels in identified engrams.
In general, the raid is very smooth with a light level of 295.
So if you do not raid, your light level will cap at 300. In order to reach the 310 gear the raid must be completed or attempted. At which point, a full 310 set would place your guardian at 310 which is the overall cap.
Now with hardmode out dropping 320, and Trials gear dropping 320, the cap is at 320 light. Some surmise that it is not possible to reach without an Artifact however this is incorrect. As the light level of your character is an average, if you never get an artifact that slot is not included in the average. The result is that several people have taken advantage of this and reached 320 already. There is probably something to be said for a tradeoff of stats (lost int,disc,str) but it is possible and achieved at present.
Best Answer
No
Equipment obtained in Year 1 will never be upgradeable beyond Year 1 maximums. The best you can hope for is that you might find a Year 2 version somewhere along the way.
Bungie did make Year 2 editions of some Year 1 gear, but most didn't make the cut. If you have a piece of gear from Year 1 that did fall into this category though, it still won't be able to go higher than the Year 1 caps. You'll have to find (or make) a Year 2 copy of that item if you want to upgrade.
Note that Infusing - a new mechanism by which gear and consumables can be sacrificed to boost stats on other gear - won't let you bypass this, either. There's two reasons it won't work:
Obviously, #1 is a killer on its own. But #2 also means that even if Year 1 items did have the perk, the best you could do is use Infusion to boost your gear up to Year 1 maximums anyway. After that, the highest Year 1 gear you'll have will have the same Attack/Defense as whatever you might want to combine with it for Infusion - rendering the combination ineligible.
Note that #2 also very well could imply that Year 2 gear will never be upgradeable to Year 3 stats, when that time comes. But that's a fairly long way from now in development terms, and a lot could change.