Yes, although you'll have to widen the spacing of the rear to accommodate a modern 130mm hub if it's below that.
You
may have to ... but it may be possible to squeeze the big (130mm) hub into the smaller dropouts by brute force. I have a bike on which I've done that. I may one day get around to permanently widening (aka "cold setting") it. It does mean that replacing the rear wheel is a bit of a performance, requiring some wrestling skills.
I use an 8 speed 11-32 cassette with friction levers and an Alivio rear mech. Works fine ... with one caveat:
I can't use the teeny tiny 11T sprocket on my 11-32 cassette. There's just not clearance for it. So I just lock out that sprocket with the HI adjuster on the mech. I don't know if you will encounter that problem.
I wonder if a 10sp cassette might be a bit pernickety to change with friction shifters, needing very accurate positioning of the lever. I don't know, I've never tried - but it might be. 8sp is fine.