It's not impossible for Mustafa Kemal-pasha to get himself killed or seriously injured, say, at Gallipoli. The Turkish nationalist movement would certainly be greatly weakened by his absence...possibly enough to be reduced into a few ineffectual protesters against the Ottoman Government?
After the Treaty is signed, ratified and enacted...well, it's a given that the country would remain under the Ottoman government, at least for some time. The large territorial concessions and economic dependence on the Entente would make the government quite unpopular, however, unless it makes a huge propaganda effort to shift the blame to the Entente and portray itself as doing the best in could for Turkey in the harsh conditions.
The ensuing period would probably be one of instability and violence in the political landscape, and might very well result in the rise of an ultranationalist or even Nazi-like party determined on reversing the "injustice of Sevres".
Turkey's role of the earliest and most staunchly secularist state in the Middle East is probably butterflied away...interestingly, I imagine the Democratic Republic of Azerbaijan might take OTL Turkey's place.
Should it survive as an independent state, and if the Entente manages to force a peace between Armenia and Azerbaijan which is relatively accomodating towards the Azeris (which I think is very possible, the Entente was quite supportive of an Armenian border far to the west, but when it came to regions like Nagorno-Karabakh they were willing to court Azerbaijan's claims), Azerbaijan might come out as a reasonably stable, secular Republic.
Pretty dystopic when ya think about it. This could have huge effects on Turkey's culture and national identity, and how they view other nations for that matter.