Not at all - MBAs teach company management and company finance. There really isn't anything in an MBA that would have anything to do with the job of corporate oversight that a board of directors handles.
The board of directors are simply large shareholders who are put there to make sure management does what is in the best interests of share holders. In most large companies, these people are mostly made up of employees of pension funds and similar institutions. Their job is to try their best to make sure the company is committed to giving their investors a return of x% and are usually there because it is conventional thinking that having control of a company is in your best interests.
Now obviously these guys have no idea what should be going on in a technology (or just about any other) company. They aren't really concerned with employees or anything like that - only with a few accounting and market figures such as return on equity, share price, potential acquisitions of other companies they have invested in, and whether or not to sell the company to others. Actually running the company or how the company works is the furthest thing from their minds.
Now, as I said above, these guys are not actually to blame. They are just doing their jobs - giving returns to the guys who have dumped money into their funds. The people ultimately to blame are you and me. We put our money in these massive pension funds and similar. We don't even care where the money goes. Each year we check our statements and say 'oh, 13% returns only, maybe I should switch pension funds?'.
As always, the problem is apathy, entitlement and 'well these guys are a big company, they must know what they are doing'.
"MBAs teach company management and company finance."
This is inherently what the board of directors does. Furthermore, you characterization of the make-up of a board of directors is not necessarily correct. Many (if not most) boards also have independent directors, who many not own a single share.
"There really isn't anything in an MBA that would have anything to do with the job of corporate oversight that a board of directors handles."
This left me scratching my head, my experience was the polar opposite of this comment. In my MBA program the topic of the board came up a number of times in finance and management classes. The board & corporate oversight were very much top of mind issues.
"This is inherently what the board of directors does."
That would be what the board of directors is theoretically meant to do. In practice it's extremely far from the truth, with board meetings being very infrequent and focused primarily on share price and dividends.
This discussion is not really about Google though: Google does actually have a very relevant board of directors with most of them being founders or directly involved in starting large tech firms. Many other companies (Nokia? Microsoft?) are not so lucky.
Interestingly enough on Google's board only Paul S. Otellini (previous CEO of Intel) and L. John Doerr (early Intel engineer and VC) have an MBA. 
I agree with your point about theoretical vs the reality of a Boards function. I should have been more explicit, I am disagreeing that Board of Directors are overlooked in MBA education. At least in my experience, the Board was discussed often.