Will using a Canon T3i as a body with the 600EX II-RT & ST-E3-RT limit the Transmitter or Speedlite from full potential use?

Yes.

But it may not matter if you don't need those features.

Does this body fully support the external equipment?

Yes and No. It does support the equipment and is compatible, but cannot do all the features in the -RT system.

It is a pre-2012 body (i.e., was introduced before the RT gear hit the market), and therefore does not support all the new features that were introduced with the -RT system. Group ID codes, Gr mode (where you can individually assign groups as M or TTL and turn groups on and off), and using the flash as your shutter remote with an ST-E3-RT on-camera, etc. are not something this camera body's menus and hotshoe can do.

It can do pretty much everything you can do with the optical wireless system, though. You can still control three groups (if not five) in Manual or in TTL with ratios. And you should have HSS, TTL, and remote power control over radio.

Will using a Canon T3i as a body with the 600EX II-RT & ST-E3-RT limit the Transmitter or Speedlite from full potential use?

Yes.

But it may not matter if you don't need those features.

Does this body fully support the external equipment?

Yes and No. It does support the equipment and is compatible, but cannot do all the features in the ‑RT system.

It is a pre-2012 body (i.e., was introduced before the RT gear hit the market), and therefore does not support all the new features that were introduced with the -RT system. Group ID codes, Gr mode (where you can individually assign groups as M or TTL and turn groups on and off), and using the flash as your shutter remote with an ST-E3-RT on-camera, etc. are not something this camera body's menus and hotshoe can do.

It can do pretty much everything you can do with the optical wireless system, though. You can still control three groups (if not five) in Manual or in TTL with ratios. And you should have HSS, TTL, and remote power control over radio.