To long; didn’t read: Yeah, probably. It’s almost certainly a good idea.
There are a few things to consider:
The obvious one. Relief is the amount of ‘bow’ in the neck.
String tension tries to pull the neck into a bow. The truss rod is adjusted to counteract that tension and keep the neck more or less straight. Increasing string gauge probably means more tension which can translate to a more bowed neck. Decreasing gauge, means less tension and the rod can compensate too much, maybe even back-bowing the neck.
It’s worth mentioning that some necks are more ‘stable’ than others. Some will take a gauge change and not even flinch. Others may need a truss rod tweak.
If you go up a gauge of strings, you need to be sure that the larger strings are not binding in the nut. A well cut nut, will generally be pretty exact for your string gauge. You might get a couple of thousands of an inch leeway but take a close look to make sure there’s no pinching with thicker strings.
And, of course, if you go down a gauge, make sure that the string doesn’t have excessive side-to-side movement in the slot. That’s a tone-sucker.
Each string’s intonation is affected by the size of the string (or the size of its core wire in the case of wound strings). Changing gauges means examining and adjusting intonation to keep things sounding as in-tune as possible.
The springs on your trem system keep it in balance against the string’s tension. Up or down a gauge and that tension changes meaning your trem will definitely benefit from a setup.
Not always so obvious but, lighter strings mean less tension. Less tension means that strings are more inclined to vibrate more ‘floppily’ (technical term). If you go down a gauge, you might find you hear a little more buzz than you’re used to. This may mean experimenting to find the compromise between action, playing style, and buzz.
Upping your gauge means more tension and, possibly, more of a fight to play. Possibly an action adjustment will help compensate.
Do I need a setup if I change string brands?
If you change brands but keep the same gauge, things are a little more complicated. Many of the mass-market brands are pretty consistent and you’ll probably be ok just changing brand.
Some brands offer different ‘selling points’ though so be aware of different tensions, materials, construction styles, etc.
Check your setup specs before and after the change, give some consideration to the points above, and pay attention to the instrument’s ‘feel’.
If you feel that anything’s altered, have a chat with your trusted tech or get your setup tools.