jQuery Mobile in a custom theme
The issue with updating jQuery manually in Drupal is that the potential arises for parts of Drupal core (and contrib modules) to break because of the change in jQuery version. The main benefit of the jQuery Update module is that it corrects the things that break in Drupal core when jQuery is updated. 

Thus, your best option is to utilize the 7.x-2.x-dev version of jQuery Update, which includes rudimentary support for jQuery 1.7.x. Keep an eye on the issue queue related to this version so that you can report and/or investigate any issues that may arise in utilizing jQuery 1.7.x in Drupal 7.