No, different internals. The 1275 gt has 9 stud head compared to the S ‘s 11 stud for example.
Cooper S had double valve springs as well. I owned both a Cooper S and then later on a 1275GT. I wasn’t a fan of the clubman front on the GT either. You could piss balls about tuning any of these engines, change the twin SU’s for a torquemaster inlet manifold with webers, LCB exhaust manifold etc., but for the fastest mini, simply dumping an Austin 1100/1300 (preferably a 1300GT) in them made a considerable improvement. I believe the Austin is/was a slightly longer stroke engine.
Oselli mini tuning was based in Oxford so very handy for me to experiment with different tuning parts.
As a side note for useless information, my 1275GT was originally fitted with Dunlop Denovo run flat tyres. When I came to replace them the run flats were so expensive that I was able to purchase four brand new Wolfrace wheels, centre caps etc and four new tyres for less money than just the Denovo’s would have cost. It was a no brainer to stick the Wolfies on.