In the main index.php file, there is the following lines:

$hc = $_zp_current_image->get('hitcounter')+1;
$_zp_current_image->set('hitcounter', $hc);

I am working on a plugin that keeps track of the most popular weekly and monthly images, and have added extra DB fields hitcounter_week and hitcounter_month. I had initially incremented these counters from a function in my theme file, but when the static_html_cache plugin is enabled, the 'normal' hitcounter is incremented (because it is called from index.php) but the other hitcounters are not.

Is there a way to hook into a page load before the static_html_cache plugin gets onto it?

How about making a custom version of the static html cache plugin and add your addition there for now? sbillard will surely later know more if this can be done via a filter (which escapes me right now).

There is currently no "filter" for page loads, but certainly one could be added. You should create a ticket with what you would require of such a filter.