No, because the relay coil gets its power from the front marker light wire, not the front signal wire. I'm talking about bikes that have dual-filament bulbs (just like tail-light/brake-light bulbs) in the front signals, like every Honda since at least the late 1960s.
The front marker light on each side is on steadily, except when either one side's signal is turned on. So, instead of the front signal flashing bright-dim-bright-dim, it flashes bright-off-bright-off. On Hondas, the right side marker light wire is the light blue wire with a white stripe.
So, because of the relay being powered by the marker light wire, the rear signal light doesn't flash, it responds to whatever happens to the brake light wire. When the turn signal is turned on, the relay drops out, and the rear signal wire is "returned" to the bike's turn signal wire.
The rear turn signal lights from the factory are only single-filament bulbs, so they only flash bright-off-bright-off. On the old Nighthawk, I converted my rear signal sockets and bulbs to dual-filament, so they're taillights, brake lights, and turn signals; what you need on the right.
If you're okay with the rear signal flashing bright-dim-bright-dim, then let the taillight get it's power from the bike taillight wire as it does now. But, if you'd rather it flash bright-off-bright-off like the front, then connect it to the same wire that powers the relay.