It maybe would, but the discomfort in your arms/shoulders/back would not be worth the benefit. And, again re-phrasing what a lot of other people said, you'd end up building core strength more than arms anyway.

10-15 push ups would likely be better for you than a day of riding like this...unless you do push ups off the bars while riding.

If you're on the bike 10 hours a day your general performance and health will probably benefit from a very basic work out and stretching routine anyway. At 10 hours I'd assume your a messenger as well; some upper body strength will also help you carry all that stuff and avoid injury in the process.