Can we run curl in tmsh mode ?

Anything is possible with the f5 (Doesnt mean you always should tho) 

From within tmsh shell use this:

run /util bash -c 'curl -vk https://f5.com'

Access to the advanced shell is restricted to users within certain roles.

The TMSH does not allow to run bash commands. Call bash shell with command "bash" for that.

Refer to the tech docs for more information about user roles and advanced shell: https://techdocs.f5.com/en-us/bigip-15-0-0/big-ip-systems-user-account-administration/user-roles.html#GUID-9C4946A7-21EA-41A1-A42E-BED65CAB0576

depending on your rights you can do

run util bash

to end up in bash

i don't believe you can do things like what you ask from tmsh