Depending on how deep homebrew access we get, it just may be possible. The biggest issue with any emulator, especially for more powerful consoles like the PSP, is if we can compile and execute code on the go. On Android it's fully possible, nothing in the system blocks it. I know it was an issue on iOS, only apps with special permissions could do it and it required jailbreaking to do, not sure how it is now. I know it was stated on PSP's site to be impossible on Windows Phones a few years back.
Now, Switch runs it's own OS not based on any of them, similair to 3DS if our hacker scene is to be believe (and why shouldn't we?), that means Switch is using NX bits to make something like that near impossible. What does it mean? That only certain parts of memory, set during execution of... whatever we use to get into homebrew (3DS example: Cube Ninja), can be used as program code areas. That is the main reason why on 3DS emulators using HBL are slower than ones running on CFW, they have much more limited executable memory (at times even being impossible to use) whereas on CFW, with kernel acess basically, all of it can be used.
In other words - don't expect a PSP emulator when we get homebrew execution on Switch, only expect it once we get a Kernel Exploit or even a CFW (as Kernel Exploits may be targetting parts not managing memory access).
And then we will have the issue of porting it to Switch itself, harware may be the same as the Shield, but the syscalls are completely different, it would need to get a major rewrite of nearly all main graphical functionality.