It doesn't look like it and I'm reluctant to tug too hard. The seat came with the toilet and I didn't see it fitted. See pic. http://www.bathroom-review.co.uk/prod/Duchy-Fistral-Close-Coupled-Toilet-Including-Seat-727439949hp.html
Agree with Bosswhite, NEVER go down a well - multiple fatalities have resulted. Having said that, from your picture it looks impossible to do. But it does sound like a soakaway if there's a pipe leading into it.
My loo was installed and the seat fixed before the pipework was boxed in behind. The seat is supposed to be the kind that closes quietly. The trouble is it does this in preference to staying up, which is no problem for female users but very irritating for males. I'd like to change it, but...