I've not personally done it, but don't see why it wouldn't work-it's not like Varian ion traps where they splash warnings all over the place about using H2.
Also, it's worth mentioning that the EPC on my 5890/5971 has an H2 option, as does the electronic flow meter on my 5890 FID/NPD. The EPC also goes nuts and shuts everything off(requiring power cycling to clear) if it can't reach the set point pressure-the manual claims this as a safeguard against hydrogen leaks(it makes a rather angry beep the likes of which I've never heard the 5890 make).
Diffusion pumps work well with H2, so you're good to go in that respect. Your pressure also sounds within reason. I'm use to somewhat lower pressures on He than you mention, but I also run an overspecced rough pump(Varian DS102 rather than the Edwards E2M2).
You PROBABLY know this, but just in case-remember that the viscosity of hydrogen is somewhat different from that of hydrogen. If you're basing your flow rate on something like HP Flow Calc, just be sure you've selected H2 as your gas and adjusted the head pressure accordingly. Needless to say, with the EPC, you need to also specify H2(I think you'll have to go through and change this on every method).
Agilent does sell a modified draw out plate meant for H2 use in the 5973/5975 that has a much larger hole. It might be worth sticking one in a 5971.
https://www.agilent.com/store/en_US/Pro ... 2589-20045