Barit - They may well do it.
Like Old Smokey, we have our normal performance chart, and a table of corrections for Mast below xxx, Mast between xxx and yyy, and Mast upto zzz.
Again as he points out, this is all good and well as long as you aren't performance limited anyway and can't take off with the penalties. That is when you need to know the exact height of the ship. Singapore does it extremely well, and NOTAM the height of the ship as well as the crossing times. ATC also tell you when it is passing through.
News Shooter - Its a perfectly reasonable question for which I hope you've managed to descern a reasonable answer. Unfortuantely despite this being a Professional Pilots website, many of the more vocal people here don't have a clue what they are talking about, having never been a professional pilot (or qualified person... some of the replies may have been from someone who isn't a pilot but is a highly qualified performance engineer) yet claiming they know it all! You will find different pilots with different opinions and that is fine too... but you'll also hear some complete garbage!
One common theme though. All the professionals have said that for WHATEVER reason, the UAL captain wasn't certain, and so delayed his takeoff until he was completely sure that he was legal and safe. Sure, he may have misunderstood the situation, and maybe the delay could have been avoided with better communication. But he wasn't sure and so he took the PROFESSIONAL (and only correct) decision to wait until he was certain and the issue resolved.