Can I use my wet-vac to shampoo my carpets?
The Rug Doctor type of carpet cleaners heat up a relatively large amount of water to a very hot temperature, and spray it fairly evenly into the carpet along with the cleaning solution, then vacuum it back out.  Although they are often referred to as "steam cleaners", the rental ones I have used don't actually produce steam, but very hot water (below the boiling point).

A wet vacuum like you indicate will do the last portion of vacuuming up the solution, but the missing piece will be the heating and spraying of the solution.  I have definitely had carpet stains that no amount of spray-on cleaner (like "Resolve" spray) would remove, but the rental cleaner would.  I believe it is the super hot water that makes the big difference.