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.
Bitcoin's price is also quite dependent on the size of its mining network, since the larger the network is, the more difficult – and thus more costly – it is to produce new bitcoins. As a result, the price of bitcoin has to increase as its cost of production also rises. The Bitcoin mining network's aggregate power has more than tripled over the past twelve months.
The receiver of the first bitcoin transaction was cypherpunk Hal Finney, who created the first reusable proof-of-work system (RPOW) in 2004. Finney downloaded the bitcoin software on its release date, and on 12 January 2009 received ten bitcoins from Nakamoto. Other early cypherpunk supporters were creators of bitcoin predecessors: Wei Dai, creator of b-money, and Nick Szabo, creator of bit gold. In 2010, the first known commercial transaction using bitcoin occurred when programmer Laszlo Hanyecz bought two Papa John's pizzas for 10,000 bitcoin.