The TSG run a stand-by system which has different levels (it used to have three, don't know what they currently do). Basically some are on duty and on patrol with an immediate response time. The number varies dependant on predicted activity / threat levels. Some are on duty but not on patrol (training, surveillance, etc.) with a few hours response time. Others are off-duty or on other duties with a response time of 16-plus hours.
G8 would have meant that those in the second and third tiers were not available to back-up the initial response in anything like quick time (though I believe some were despatched back down the M1 pretty damn sharpish). Whilst the immediate response tier would be "usual", I would not expect it to be enough to deal with a four site incident of this sort.
In short, therefore, I would think that the absence of large parts of the TSG
probably DID affect the immediate response and unubtedly affected the speed with which the required additional resources could be made available. That said, the effect was probably pushed down the chain to local policing pretty quickly, with officers pulled from other duties on divisions across the MPS and sent to assist. If this had been a public disorder situation this would have meant a poor response as they would not have the level of public order training / equipment as the TSG but for the sorts of duties required here it would make no difference.
(ETA: All of the above relates to the REACTIVE response. As to whether their absence helped the bombers get through - I would say a definitive "No", their presence would not have made any noticeable difference to the levels of visible policing and there is no suggestion that there were any specific preventative operations on which they would have been deployed. As for whether the bombers decided that their absence would make a difference - who can say?)