I've done it here in Long Island (salt water). No real problem with corrosion,(mine is on a mooring not in a marina with shore power) but marine growth is such a problem that I may try an outboard next time. The anti fouling paints for aluminum don't work that well and if you are in a high fouling area it can be bad enough that you will have to pull the boat and clean it every 3 months or so. If you are not in a high fouling area then it is feasible as long as you are diligent about maintenance. I/Os are high maintenance, the highest of all marine propulsion systems. They will NOT forgive a lack of maintenance. Certain items if not checked regularly will cost you dearly (manifolds/risers, bellows, gimble bearing, ujoints). If the bellows leaks on a Merc or Volvo (SX style and newer unlike the older Volvos) it will rust the gimble bearing, ujoints, and let water in the boat. The drive should be taken off once a season to check the bellows, gimble, joints, etc. I do this every year and it has helped me avoid major repairs. Keep in mind also that the sterndrive unit is in the water all the time and if a seal leaks you will get water in the drive which will ruin it eventually if not corrected. This is why I change the gear oil each season and check for water in the oil. If not I store it in the garage for the winter, if so I take it to the mechanic to get it resealed.
I/Os are really common on smaller boats and on smaller cruisers they are the most common propulsion system out there. Probably because they save some space compared to a straight IB or V-drive and are easy for boat manufacturers to install. An outboard is better suited to salt water storage but they can have problems too.
If considering a newer boat Merc's SeaCore system is specifically designed for salt water.