KS eteni cartridge question

Hi All - I have an aging KS eTen-i that is quite slow to return. The cartridge isn't serviceable, but from pictures, it looks like there is a Schrader valve there. I'm wondering if I could pump that up with my shock pump? If that would buy me ~6 more months of operation, I'd be happy with that. This is an old bike, and I'm just trying to keep it going for a little while more.

I haven't taken it apart to inspect it first hand yet, because I'm hoping to only take it apart once. Thus, if it's not actually a standard schrader valve or somehow it just doesn't work to put some air into it, I'll just order a new cartridge.

I have changed my seat on this bike, and the valve is not accessible from the top. You have to pull the cartridge out of the bottom of the seatpost, it's a relatively major surgery.

Thanks for any info.