Is this even possible?
Why not? Transfer it to your favorite exchange, buy bitcoin, done.
You might influence the price slightly (~0.5% on bitstamp).
You would probably want to transfer to the most liquid exchange that is reputable.
As it stands now, if you were to buy $100k worth of bitcoin, you would cause the price on bitstamp to rise 1.5%, but on average the price you will pay is 1.17% above the last price. If you were to buy $100k worth of bitcoin on bitfinex, it would cause the price to increase 0.77% and on average would pay 0.47% above the last price. If you would to buy 100k on coinbase then it would cause the price to rise about 2%, and I am not sure what your average price would be.
AFAIK there are no limits as to how much you can deposit at bitstamp and bitfinex, and you can have your limit on coinbase raised to pretty much however much money you have as long as you can show proof of funds, although your ACH deposit limit is not going to be raised above $10k per day
