Yes you can add any tool chain on your device, you just need to add it to your Yocto image then you will have it in your board.
We did the experiment some time ago and concluded the use case was not relevant for this platform (requires a lot of space and some computing power we better have on host).
Cross compilation is really convenient for easy and rapid development cycle especially with the developer package (to work on the BSP or build applications based on openstlinux distribution).
To build your own distribution and if Yocto is a worry for you, you may also use buildroot: see this excellent article from one of ST partner https://bootlin.com/blog/building-a-linux-system-for-the-stm32mp1-basic-system/
