A few years back a plumber I got in to install a central heating system just took my old tank away as some kind of perk, never even asked ! Not that I had any use for it, but damned cheek anyway. And on other occassions things I've been assured will be taken away from the builder just got left. Tradesmen eh ? Tsk.
No I can't see a hot water tank is likely to have asbestos, although I am aware some come with their own installation, so I suppose it's just possible. But I suspect they started coming with their own insulation after it was known asbestos was a health hazard, so it seems unlikely.