Base management can be handled with sand, lead, or even cat litter. Oh, you mean BASS management...
No, plugging the port will not change the amount of power needed by the speaker. As jaxvon already pointed out, you will lose some output, causing you to potentially actually have to turn it UP slightly. So, while bass response was reduced, it did not actually modify the frequencies being sent to the speaker, so it will still attempt to reproduce them.
The sub shouldn't have a problem with a full range signal as long as it has a low pass filter.