How long is a piece of string? It honestly depends. Are you planning on camping/hostels and eating on the cheap (making your own food or buying from a supermarket, with the occasional meal out)? If so, yeah, it can easily be done on that budget. Do you want to stay in a B&B/hotel and eat out every meal? Probably not.
Cycle touring can be as expensive or cheap as you like. It depends entirely upon your requirements. I'm happy in a tent, cooking for myself day in, day out. Others wouldn't even consider stepping outside the door without a fully planned itinerary and targets for accommodation daily.
Everyone has their must haves I think. Mine spacious tent, don't care about weight saving tiny weeny tents, always carry pasta and pesto for adhoc meals if no shops about, more clothes than I need, and a solar shower. Others will be aghast but as I say, everyone's got their must haves.