Yes displaying a Google Map counts towards API usage, as seen
here:
http://code.google.com/apis/maps/faq.html#usage_mapload
It says:
A single map load occurs when:
- a map is displayed using the Maps JavaScript API (V2 or V3)
when loaded by a web page or application;
- a SWF that loads the Maps API for Flash is loaded by a web page
or application; or
- a single request is made for a map image from the Static Maps
API.
- a single request is made for a panorama image from the Street
View Image API.
The degree to which a user interacts with a map once it has been
loaded has no impact on the usage limits.