Ok all you "no STI" dudes! Thank you for your opinion but, to the OP:

GO FOR IT!

You don't need to cold set. Going from 126mm rear spacing (your Trek) to 130mm (8+ speed era) is nothing, and requires just a touch of prying (the dropouts) with your thumbs as you use your fingers to pop in the rear wheel.

I have found that a modern groupset and modern wheelset can do a lot to reveal the "true nature" of a steel frame in some cases. I think, since your Trek has a lot in common with more modern racing bikes due to its geometry, it's not a thematic stretch. I've been doing this sort of thing to a lot of frames, and thoroughly enjoy it. Quill stem to 1 1/8" stem conversions to run modern 31.8mm compact handlebars is another thing I've done. Di2 conversion as well.

Get in on the madness, er, fun!