Yeah, most other WiFi shields use another microprocessor to handle the intermediary tasks. The WINC1500 shield gives access to the chip to the microcontroller (MEGA2560 in this case) via SPI so will use a lot of memory keeping the library loaded.
The MEGA has the same flash but reduced RAM compared to the suggested M0 Metro
So should be able to hold the libraries well. You might have to be careful when calling for information as the MEGA has 4x less RAM and will easily fill up.
SD cards almost always interface with an Arduino via SPI, and this WiFi shield does the same, so stacking boards separately wouldn’t have any effect other than changing the form factor.