Yes, although this might not be the cheapest way to go, depending on how many people are in your group.
We always fly in the night before and stay at the Hyatt at MCO. It's right in the terminal, so you just grab your luggage and head up there. No need to wait for a hotel shuttle. It's also a bit more expensive, probably between $79-$129, depending on how far out you book and what deals are running at the time. You can get a cheaper deal at an off-site hotel, most of which have shuttle service to and from the airport.
Check-in for the
DCL busses is in the Hyatt lobby on the morning of the cruise, another reason we like to stay in the Hyatt. The transfers are $49/pp.
You can usually rent a car cheaper. Here's some good info on car rentals:
http://www.dcltribute.com/carhire/
Depending on how early you arrive in Orlando, you might want to rent a car and drive to the coast the day before the cruise.
You can also rent a towncar or limo and transfer to the port this way. If you do a search on "towncar" on this board, you'll get lots of info. I've never done this, so don't have much to offer in the way of advice.
In the end, we go with the transfers because we like the convenience. For the same reason, we stay at the Hyatt rather than an off-site hotel. In the overall scheme of things, it may cost maybe $100 more, but that ends up being only a small percentage of the entire cost of the trip, so we figure it's worth it for the added convenience.