Normally, a gizmo with a 5V USB host port (such as a computer) can be expected to supply up to 500ma (1/2 an amp). That is a published USB standard. I've got a little battery brick with USB ports on it, and I use it to power an H120 or a MR1. The recorders have their own internal battery so this brick "helps keep them charged." When you boot up the recorder and the hard drive starts to spin up, it uses more than the 500ma (MR1 is quoted as more than 1 amp), but the recorder's internal battery makes up the difference in the short run. If you have a device without an internal battery, and you are JUST running it off the USB port you have no built in shock absorber, and depending on the device you might exceed that 500ma rating and it might drop out. Hard to know until you try it.
Then there is the whole "ground loop" consideration... I see it mostly in industrial equipment. I doubt it's an issue here, just pointing out that when you take 2 devices that aren't at a common ground, and you decide to tie them to a common ground, you create a potential problem (no pun intended). This is the main reason I don't try to run different stuff off the same battery.
This is all generic, and none of this specifically pertains to the Tekkeon, but I expect the same rules apply.