No. Between heroes left in play from the previous wave, and heroes prepared in your deployment stack, the maximum number of heroes you are permitted to have is two heroes per wave (except Wave 1 which is restricted to just your starting hero).
Even if a hero is defeated in the middle of a wave, there is no opportunity to put another hero into play until the next wave.
Units, in general, cannot be staged in the fortress. If they are prepared, they must leave the fortress at their earliest opportunity (when they are on top of the deployment stack, and there are valid hexes for them to move to).