@blair The effectiveness would really depend on how much data you will be storing and usage pattern of it.
You can checkout EFS option and this thread as well.
If I understand your correctly - you want to snapshot and terminate instance every time, in this case - yes you have to pre-warm EBS each time you start instance.
But you can just stop it while not using it, change instance type and start it when needed. EBS volume in this case remains on the same place and no prewarming needed. Yes you will be charged if you go beyond free tier on EBS Gb/months.
P2 does not have any CPU usage limitations, but EBS behavior still applies.