My rudimentary understanding of this would allow the API to dedupe/merge leads as they were added to Marketo.
Well, once you're using the Merge API, the implication is that all leads (the "winner" or target lead and the "losers" or contributing duplicate leads) are all in the database already.
If you want to pre-check a brand-new lead, you might first do a get using the Get Leads API, but you wouldn't need to merge leads per se (except in the theoretical sense of merging new external data values into an existing lead). You would just choose a lead to update.
If you had a list of identified duplicates, you could pull the list members out via the API, assemble the winning values, then merge them back in using the API.
That would be your Engagement Manager or Customer Success Manager. Customer Support doesn't support or initiate that process, it is a Professional Services engagement.
There's another service called Auto Merge which is the automated way of addressing duplicates ongoing versus the one-time merge with Easy Merge. We are in the process of working with our CSM and Professional Services team to get Auto Merge launched. So far it has been really simple and quick to get setup.