For your first question, the easiest programs to install from the heap are the conspiracy breakers. I saw some janky but functional builds using Scheherazade (which has rotated) and Sahasrara (C&C) to install a heap breaker for free on pretty much every run where you encounter ICE, and pick up a draw in the process. Stuff like Cold Read could potentially also fit into such an engine. Getting clone chip influence free might help that setup a little bit, but it’s probably offset by the loss of Scheherazade. Reaver and Wasteland are probably worth looking at if you plan to trash programs so that you can reinstall them from the heap.
As for your second question, the best comparison is probably to Geist. You can more or less omit draw effects from your deck when building Geist, because his ID triggers enough to make up for it, even if you just put in generally-good cards that trash and don’t go full build-around.
With Exile, you can realistically get maybe 10 triggers over the course of a game between heap breakers, clone chip, scavenge (good with lady!) and test run without building a big wacky engine. Unfortunately, those are probably going to be concentrated later in the game (at a minimum, you need to at least get a program in the heap before you can start triggering), which is when draw is less important.
…and if full build-around, by the time you get your engine up, why are you still hurting for draw?
So I think he’s not looking good. It’s not that drawing on heap-install is bad in itself, but it’s probably too limited in when it happens and how much you can capitalize on it to be better than, say, Jesminder Sareen.