Legalised betting is definitely a factor, but perhaps because its legal here its not a big deal, whilst of course plenty of people do bet on games, in % terms its a very small minority of people and even then mostly for fun rather than serious bets.
Legalised gambling of course increases the prize pots through sponsorship, which helps, but before the betting companies starting putting down cash it was the cigarette companies (which isn't allowed now in Europe), so I think even if gambling was banned snooker in the UK at least would be fine (as someone else would step up to sponsor events).
I'm under the impression (and may be wrong) that there is a much larger betting culture in parts of Asia and it may well affect viewing figures there if you stopped gambling.
Anyway, the top snooker players are all multi-millionaire's, that is why its a popular game...with good prize money on offer a lot of people want to play, hence a lot of people come into contact with the game and there is general interest.
Also, perhaps a big factor is that the WC and the Masters are on free to air TV not cable/satellite, so everyone can watch for free.
I agree that gambling is not a big factor in snooker's success. Snooker took off commercially in the early 80's, and the betting companies have only been significant sponsors relatively recently.
And gambling is not going to be pool's saviour - it is a chicken and egg situation: The big betting companies are only interested in activities that have reached a high level of success. Until that time, the risk / reward balance does not work.
Legalised gambling will not make pool a success; and it can only play a small part in sustaining it after it has become a success due to other factors.