Can you run 52/39 chain rings with an 11/32 cassette?

Yes, you can, although you'll need a longer chain to go with it.

The important thing here is the capacity of the rear mech you're using. However, since your bike already has 50/36 11-32 gearing, changing the chainset for a 52/39 actually reduces the amount of chain slack the rear mech has to deal with (52-39 < 50-36), so there shouldn't be any problem.

Just remember to adjust the position of the front mech (move it up the seat tube) to accommodate the larger chainrings.

Answer: Yes.

I have a 1989 Cannondale 3.0 road race series. It has a 52/39 with an 8 speed 11-32 cassette and a Sora medium cage rear mech. It shifts good and also can run down hill pretty fast and climb steep hills. Was thinking about switching to a compact but, still have my doubts. I love it.