Subscription to User-saved searches
Conceptually the business logic you want to complete is possible using Drupal. Finding a way to make this scale to a very large website -- I leave as a project for you.

Start by looking at Saved Searches and Views Saved Search or Views Save. These modules let you save a search with a simple name for later re-use. Some of these modules allow per-user saved searches.

You could then create a Queue using the Queue API in Drupal to periodically process the resultsets of these searches. Or even use the Relation module to store heuristics on these resultsets.

Create a cron task using hook_cron or Rules Scheduler to periodically process the resultsets and have Rules to send off emails about new changes in the saved searches. Functions like views_get_results (if you use views_saved_searches) can help you to get these results.

So in general yes it's possible with Drupal -- scaling all this to a very large amount of  users is either an infrastructure problem or something (i think) "Drupal" shouldn't do in the long run ...