To answer your concerns as simply as possible, yes, conditions can cause lag in a map even if the trigger isn't firing. With the right (or wrong) use of Bring conditions for example, you can bring a map to a grinding halt even if the trigger itself isn't firing.
I would like to think it works the way you're thinking it does, checking conditions in order and moving on when it gets to one that's false. To answer your question about Bring vs Command, yes the Bring condition causes more lag than Command does. If you need to check at a specific location there isn't much you can do about it though.
Using too many Bring conditions over too large of an area will start causing what appears to be lag. It is actually a memory leak, caused by the way StarCraft handles the Bring condition. If you run into this issue, there isn't much you can do about it since you clearly need Bring for specific locations.
The first thing you should do is troubleshoot your map. Make a copy of the file, and in the new map, change all the players except yours to Computer. Start game, make sure the lag is still there (if it's being caused by triggers it should still be there, if it's a memory leak from Bring conditions it will definitely be there still).
Once you've verified the lag occurs on this map, start deleting triggers in bunches. Delete the first 100, save. Test it again. If it still lags, delete another 100. Keep doing this until it stops lagging. Now you know the problem is within those 100 triggers. Put the last 100 triggers back (copy from real map, have 2 test maps you alternate between, or however you want to handle this). Now repeat the same process except delete the triggers 20 at a time until it stops lagging. Put the last 20 back.
Continue this process with smaller and smaller intervals until you figure out exactly what's causing it. If you can remove the problematic triggers, or workaround them, then do that. Try to reduce them in number as much as possible.
If you can't afford to remove the triggers, then I would suggest trying what you're already considering, placing a condition in front of the other conditions that is false so it won't check the conditions after it. It's a sound idea based in logic, now you just have to hope that the way SC handles it is similarly logical
Post back after the troubleshooting process and let us know what you found to be the problem.