Should be no issue. Meraki is scalable. As long as your WAN link has the necessary throughput to spare for the out-of-band management connection to the cloud (it needs 1kbps per Meraki device). That's really not that much. And the cloud's performance scales easier than on a physical controller of course.
Meraki also has L3 roaming support if you need it. But for those numbers you might need an MX (or a pair of MX's for redundancy). You'll need at least MX250's for the amount of tunnels needed so make sure you size that well using the numbers found in the datasheet:
https://meraki.cisco.com/lib/pdf/meraki_datasheet_mx.pdf
L3 roaming is described here:
https://documentation.meraki.com/Architectures_and_Best_Practices/Cisco_Meraki_Best_Practice_Design/...
And also check out this article about high-density wifi deployments:
https://documentation.meraki.com/Architectures_and_Best_Practices/Cisco_Meraki_Best_Practice_Design/...
Also regarding the need for L3 roaming. Do you really need students to be able to walk between buildings and keep the connection. How many students will care that they lose a skype call when walking between buildings?
Also, for a large deployment like this, please reach out to your Meraki Partner or Meraki SE to get the design validated.