Yes it can—but it won’t do it much good. The reason is that Google’s servers aren’t fit for solving the Bitcoin mining problem in the same way that ASICs are. For reference, if Google harnesses all of its servers for the sole purpose of mining Bitcoin (and abandons all other business operations), it will account for a very small percent (less than 0.001%) of the total mining power the Bitcoin network currently has.
This is particularly problematic once you remember that all Bitcoin transactions are permanent and irreversible. It's like dealing with cash: Any transaction carried out with bitcoins can only be reversed if the person who has received them refunds them. There is no third party or a payment processor, as in the case of a debit or credit card – hence, no source of protection or appeal if there is a problem.
In January 2009, the bitcoin network was created when Nakamoto mined the first block of the chain, known as the genesis block. Embedded in the coinbase of this block was the following text: "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks." This note has been interpreted as both a timestamp and a comment on the instability caused by fractional-reserve banking.:18