All malignant cancers need to maintain their telomeres in order to possess one of the hallmarks of cancer, limitless replicative potential. In rare cases, some cancers which do not maintain their telomeres, such as a subset of neuroblastomas, spontaneously regress. Tumours have 2 methods of maintaining their telomeres; one is expression of telomerase (hTERT) and the second is alternative lengthening of telomeres (ALT), used by a minority of cancers (but up to ~20% in certain cancer types). 

In my experience,  tumours which use telomerase to maintain their telomeres have shorter telomeres than their matched normal tissue.  Whereas the remaining 10-20% of tumours, those that maintain them by ALT have telomeres 1.5-4.5x longer than those from matched normal tissue. I have seen this both in my data on various brain tumours and recently at a conference where several scientists presented data on telomere length in normal colon, polyps and colon cancer.

Telomere dysfunction in general has been implicated as a potential initiator of genomic instability, but I have not seen a study comparing if universally tumours with shorter telomeres have higher mutation rates that tumours with longer telomeres such as those that use ALT.

Various cancer types and tissues have intrinsic mutation rates and there are many cancers that have very low mutation rates and no recurrent mutations. Therefore I would be careful when stating anything about the number of mutations required for cancer as there are many cancers where mutations do not seem to be the cause. Even high mutation rates seen in certain cancers could be a late event of tumourigenesis, and perhaps initiation of telomere maintenance is a later even during tumour formation.

In the last few years there have been studies looking at hTERT promoter mutation as a potential driver of hTERT expression in cancer.