Will derailleur work on this freewheel?
 

I have an old touring bike group (Shimano 600 arabesque) with triple front 52 45 39 and a 5 speed freewheel with 32 as the big on a 27" wheelset. I want to put the group on a newer bike that is built for 700c wheels and will be using a different wheelset. Can I use a 7 speed freewheel with the biggest of 32 and still have the rear derailleur shift correctly?

There is no clear yes or no answer. It depends on the geometry of the particular derailleur and on the derailleur hanger.
Try it and see.
If there is an adjustable "B" screw it may adjust the derailleur far enough to clear the 32, or it may not.
It may be possible to replace the B screw with a longer one.

If you're asking whether a 600EX long cage rear derailleur (see here) will shift to a 32-tooth cog- well, maybe. Shimano spec'd that derailleur for a 28-tooth maximum, but they've always conservative. It might work, it might not.

I always had trouble with the upshifts with that derailleur. The minimalist inside cage (aka Hatch-Plate mechanism let the chain come off the upper pulley too easily. This eventually caused the chain to tie itself around the cage, breaking the lower cage plate. It might have been my combination, but frustrating nevertheless.

The bike's a Half Step Plus Granny.
A medium length,,,derailler cage at one time could handle a 28 tooth freewheel.
A 5 or 6 speed 14-28T 0r 14-30T freewheel used to be pretty standard on many bikes. It depends, if if said derailer,,dosen't have a position,or B screw or barrel adjuster a newer swap would improve the bike. Chris

RD's are labeled all over the map - and ever accurately. So it's hard to tell. Best advice would be to know how to adjust a RD - then try it. If it won't work, get a mountain-bike RD like Shimano makes.

Do let us know, please. This is info many folks come into here to ask.