Is it possible to re-attach addons so that players can still maintain the ability to build units, or be able to disable lift-off while still being able to build units?

...I don't quite understand. Are you asking the way to make a Terran building build its addon units after lift off, and how to prevent players from lifting off?
To prevent players from lifting off, place a location on the buildings, double click the location, uncheck "Low Ground", "Mid Ground" and "High Ground" then run a trigger to remove the building and place a new one if the player brings the building into the location.

Your question, or specifically what you're trying to do, is not clear.

In-game, the only way to have an addon attached to a building is to have the add-on sitting next to the building. You can't have an add-on at one part of the map, and a building in another. Once the building is lifted, any previous add-ons attached will be disabled. You can create sprite disabled buildings that prevent lift-off, however these won't be able to build units and probably can't have add-ons either. There is no other way to specifically disable add-on (maybe having the air-space above the building completely full will prevent it?)

You can however pre-place such add-ons in Scmdraft2, and you can also pre-place add-ons that are active for a specific player (normally they turn to Neutral if you lift the building). In the former case, if the player lifts the base building, the add-on will go back to nuetral. In the latter case, if they create a base building next to the add-on, and then left it, the add-on will go back to neutral.

To make a long-distance attachment in Scmdraft2:
1. Place the base building and the add-on so that the graphic attaches and the green add-on line is created
2. Select either the building, or the add-on, and press Ctrl-Arrow key to move the building by 1 tile around the map - the green line will stay and get longer, and the add-on will still show the 'attached' graphic. You can press Shift-Arrow key to move the building by 1 pixel instead of 1 tile.

To make a player-owned add-on without the base building:
1. Create just the add-on for the player
2. Under Options - Units, make sure Addon Autoplayerswap is enabled.

I just want the players to maintain the ability to build any type of unit— whether it's re-attaching the addon, preventing lift-off, or another method.

Well re-attaching the addons would be easy enough with triggers as long as the building is centered correctly in the map and by the triggers. Anti-lift off is easy. Discourage that by naming the building something like: lift-off= deaths and having some text display calling them a noob or something seen that in maps.

Hmm... could have sworn before that recreating buildings didn't reconnect the addons. Maybe I did something different before. Anyway— finished is a topic, and it is.

By the way: http://www.staredit.net/files/609/

I did just that (among other things) in this map.