Yes. Custom URL and params.
The problem I was having with the stock button was that if the current month had no events, the export button would export an empty iCal file, even if you navigated to a month that had events. (For example, It is July and July has no events…Navigate to September (which has events) and click export -> export button creates empty iCal file…)
I’ve found a work-around that seems to be working okay for me — I hid the stock export button using CSS and added a static HTML button in Events > Settings > Display > HTML after content. My export button exports a whole years worth of events.