training indoors in a suit?

I find the tie gets in the way on flip turns    

j/k.  No, it's not a good idea to use it all the time, for a number of reasons.   Practically, you will shorten its life.  Performance wise (although I suggset jammers rather than running shorts), a suit will compensate for your weakensses, and you will either never discover them, or will be less likely to work on them.   Number of other reasons, but those are the primary ones that come to mind (not to mention you'd get too hot).

You should practice in open water or the pool with it on prior to your first race though.

The people you see might be in swim skins or speedsuits

the chlorine will eat away at your suit and soon it will be see thru.  I practice in a regular suit, so on race day I feel faster in the water in my tri shorts.

That's great info thanks.

I was hoping it might be something like that.
I own plenty of lycra bike shorts, but I would never go out on my bike or even to a spin class without baggies over the top, can you tell I'm a MTBer nor a road bike guy? 
guess I'll have to consider something tight for the pool swim at some point though...

swim/train in my normal suit, race in my tri shorts/suit..

It's not a bad idea at all to at least once before a race train with the equipment you intend to use... so go ahead and take a swim in that suite (just make certain that you rinse it in lots of clean water right afterwards and then go home and wash it out good). Same thing goes for race wheels, aero helmet, race running shoes (flats), etc. Get used to the feeling so you're not having any unpleasant surprises come race day.