Does F5 Support IPSEC over GRE ?

There will probably be some issues here. This article describes the situation which is the opposite analogue to your position:

K16093: An IP tunnel built over an IPsec tunnel interface will not work

IMHO much of the issue in that respect will apply to your situation also since tunnel objects on BIG-IP act similarly to VLANs.

You would potentially run into a problem with your self-IP since BIG-IP doesn't have a directly analogous concept to Linux point-to-point links.

I'd be inclined to set this up in my lab to understand the reality of it since as long as your IP addresses are adjacent and the lower one's last octet is a multiple of 2 you may be able to configure a /31 subnet for the self-IP to get this to work.

Whether it'd be considered supportable in production if it ran into difficulty and in the light of the above KB article would be another question entirely.