Is it possible to run a Drupal 7 site without jQuery?
jQuery is part of Drupal core - and because of this, you can't tell WHAT contrib modules are going to be using it.  Well, you can, but it'd involve checking any included scripts of any module. Also, you wouldn't remove poll.module or blog.module just for server side performance if you're not using them - I would suggest the same applies to jQuery.

I don't think removing jQuery is an option at all realistically, it's not worth the hassle of even trying.

The following, however, are MUCH better options.

For starters, get your hands on the jQuery Update module if you're not using it already. One of the best things you could do to improve jQuery performance is use the most up to date version of the library possible.

Next, try Boost:.


  Boost provides static page caching for Drupal enabling a very
  significant performance and scalability boost for sites that receive
  mostly anonymous traffic.


or Varnish if you are on a dedicated hosting plan and have the resources to set it up (Drupal module here).

Serving static HTML pages will take substantially less time, than serving a full dynamic page.

Lastly, if it's a REALLY simple site, evaluate whether or not you even NEED Drupal?  

Could you perhaps use a Drupal back-end to manage your content and combine it with the Services module to supply your content to a more performance focused site with a lightweight framework such as Laravel?  I've run into situations before where I've used Drupal because "IT'S WHAT I KNOW DAMMIT", where I could realistically have used a much lighter framework and removed a lot of overhead.

EDIT

I forgot to mention the performance tag.  Check out other questions tagged with performance and there will be a plethora of people who might have similar front-end performance issues/ideas!