Note that statically checked inline asm is very achievable, so those folks who do constant time crypto by concealing their math operators behind inline asm will get what they need.
But I guess you really want the OpenSSL out-of-line assembly to work?
Yes. And that code generally does not invoke the allocator or stray out of the bounds of the given buffers, so at the very least you could mark that assembly as trusted for this mode.
But see https://fil-c.org/runtime
It's really about creating an FFI for Fil-C, because Fil-C has its own calling convention and symbol mangling. It could be a lot of work.
And, worst case, it ends up being a footgun
If I made the assembly memory safe under Fil-C rules by running it through a transform that inserted additional instructions but did not otherwise change what was happening, would you trust that it's still constant-time?
If a user is doing onion wrapping, they don't want you to branch on the code data either.