Could I boil vegetables now (potato, beetroot etc.) And then roast them a few hours later? This would be convenient, but would it effect their taste, texture etc?
Yes, this works, as long as you don't boil them too long. The idea is that by the time they get roasted properly (e.g. your potatoes are browned on the outside) the inside is only just cooked, not overcooked. I'd aim for very roughly half cooked, starting to be pokeable with a fork but not actually tender.
For flavorful things like beets, you may lose some flavor into the water, but they should still be quite good. If you want to avoid this, though, you can just steam them instead, or even microwave. It's not really much more trouble than boiling! If you do this, and get the timing right, it won't really affect the taste or texture much at all compared to just roasting.