Yes, if the electric starter works from the push button, that means the handlebars are grounded. Also if the battery has the power to crank the engine normally, that means the battery is in good condition capacity wise.
If your flasher relay is the thermal type, the battery can be fully charged (12.5 volts), and yet the 12.5 volts may not be high enough to operate the flasher relay. Stock type thermal flasher relays sometimes need 13 volts in order to make the flashers work.
I tossed out my stock thermal flasher relay years ago, as it became a safety problem. It would sometimes stop flashing when I was sitting waiting to turn at an intersection......................very dangerous. I now use a Tridon HD12 flasher, because it will reliably flash the signals with voltage down low such as 12.0 or even 11 volts.