For the GBA or for the battery in the Omega?
I am guessing the former.
Short version. No, and obviously GBA mode on the DS is still GBA mode and it was the DSi before we got proper measurement anyway.
Uptime is more doable. Two main approaches being if you have real time clock on your cart then should be easy enough to ping it every so often and note that. Then either do something like the in game readers/menus (I know they were mostly for the DS but something could be done for the GBA) or fiddle with savestates.
Longer version. You can bump the power draw up and there is usually a little light somewhere that will indicate low voltage.
If they really wanted they could find a way to add a small routine that would take over, run minimal current draw and then bump it up (add sound, slam the CPU, do all the DMA reads, if you can do something with the cart's own FPGA or whatever to increase draw then fantastic...) to get it to pop up the voltage on the low side low light and calibrate it accordingly either for that system or more general ones (harder there as a spanking new SP battery is probably different to a "under perfect conditions on an original cart this decade or more old knockoff battery"). Probably would be hard to do for a fully charged battery but that would also be information.
This is all a lot of work for "I know I am going to have to charge this if I play for more than about 6 hours".
