Cannot handle it, and doesn't have to handle it. A Tesla will only pull the full 350kW for 2 minutes in a charging session, and sessions average ~20 minutes. And even when the station is full, there are always stations pulling 0W because they're switching between vehicles et cetera.

But if it did need to handle that level of instantaneous load, it would be straight forward to supply. 98 Tesla's worth of batteries on site could do it. The grid tie is substantially smaller, because the grid tie only has to handle average load, not instantaneous load.