Not sure as I mostly use 3/8" plexi and that is only available in clear FAIK. That plus its tough to think of any sales application, other than random novelty, for a colored plexi sign.
Any tinting mutes light transmission, I have tried tinted lexan and is nearly useless for edge lit signs ,,, But tinted lexan is specifically designed to block light transmission so that shouldn't have been a surprise for me. I'd say for sure stay away from the darker tints, attempts to light will be entirely underwhelming.
Wouldn't hurt to try if you like to experiment and have a supplier, I'd say keep your expectations low and only use white LED's. Wouldn't seem to make much sense, for instance, to try lighting a light blue or yellow tint with a red or green LED.
To summarize, I think the lighter tints would be doable. Yellow for example would indeed look yellower than clear with a yellow LED, but won't be as bright and of course, you are limited to that one color.
Also, wouldn't not try going thinner than .25, .125 is tough to light up and can be tough to make bases for.