Yes. Over years/decades, (assuming for the moment there are only two types and ignoring the autoimmune process) type 1 and type 2 move towards being the same condition, in that in T2 the beta cells eventually pack up completely, whilst type 1s gradually become more insulin resistant.
Like everyone else (diabetic or not) Type 1s are more insulin resistant when the body is under stress, hence our bs/insulin doses climb when we get flu etc, so there's no reason that can't happen due to excess weight, steroid treatment etc.
That said, there are veteran T1s here still on small doses, so the above clearly isn't inevitable. Partly the luck of the draw I guess, like complications.