Not in my experience, nor that of my friends who got offers.
My typical friend who got a Google offer, already had a bunch of other offers by the time their Google process finally completed. Then the Google offer came in and it was typically higher than most or all of these outstanding offers. Often substantially so.
However, if you have an outlier offer that is based on some theoretical equity valuation ("an extra $1m in stock options based on our last fundraising round"), Google will not match it.
Frankly, they don't need to when their initial offer is already higher than most other options, and far safer.
Also from what I've seen, Google won't just match other offers, but they do have some specific companies whose offers they will match, like FB. FB is also one of the few companies that may offer you higher comp than Google.