Does the compressor inlet size, i.e. 2.75" or 4", have any effect on performance?

A bigger housing flows more air. A smaller housing flows less air.

A TO4S housing (4" inlet) is worth around 40 horsepower over a TO4B (2.75" inlet) in the context of a 60-1 wheel. A TO4S housing upgrade to a T3/TO4E turbo will typically net you 15-20 peak horsepower at the cost of a bit of efficiency.

I am getting a GT3071R turbo with a T3 style turbine. The compressor housing is T04E frame size with 2.00" outlet. Compressor inlet is available with 2.75" or 4.00" inlet. So does the 4.00" inlet flow more than the 2.75" inlet? thx for the help!

You could probably squeak a few more ponies out of it. If you can fit a 4" filter/pipe in there, by all means go for it.

Thanks for all your help should have all the pieces installed in the next couple months, I'll post up some dyno sheets and let you know how it turns out!