Just do it! My general philosophy for projects like this is: If I already own parts, I'll bolt them up and see if I can make them work.

1. Those friction thumb shifters will make almost any derailleur work. It may not shift as slickly as a modern system with all matching parts, and you'll have to fish around for the sweet spot where you get no derailleur rub, but it'll work. All those matching parts issues only came up with the advent of index shifting.

2. Somebody brought up the chain slack with a triple crankset issue. In real life that's all but non-issue. Most riders only use the granny chainring with the largest 2 or 3 rear cogs. If that's you, the chain slack issue won't come up while you're riding. Problem solved.

I think that tinkering with a cheap old bike like this is an excellent opportunity to learn about how bikes work. If (when) you make a mistake, think of it as tuition in the school of bicycle mechanics.