Ideally you want to run speakers that are specifically designed to work together. No guarantees that a GK will work well with a Fender.
If there is a matching cab for the Rumble, I think that would probably be the best option, but it can depend on the sensitivity ratings of the speakers, which AFAIK are not published for the Rumble series.
With matching cabs, when you double the drivers the sensitivity rating goes up about 3dB.
The impedance also is cut in half, which has often has an impact on the amount of power a solid-state amp can produce.
With 8 ohms the Rumble makes up to 350W and with 4 ohms the Rumble makes up to 500W.
Decibel Difference from Increased Power = Log(500/350) x 10 = 1.5dB.
Total Calculated dB Increase 3dB + 1.5dB = 4.5dB. This is a noticeable increase in SPL
Since the GK provides it's own power, it will not reduce the volume of the Rumble. But I don't expect a 110 powered by 100W to make a lot of difference, although it may...IMHO try it and judge for yourself.
To help you understand how it works:
When you have two identical cabs tight packed together and playing at the same level, you get approximately +6dB from acoustic summing. In other words if both cabs are producing 90dB individually, the combined output is about 96dB. Maximum acoustic summing occurs for frequencies where driver spacing is less than about 1/4 wavelength...I.E. at low frequencies, which have longer wavelengths.
If the cabs are not identical they may not integrate well. Essentially they fight at some frequencies rather than working together. This is do to differences in group delay and phase angle.
If the SPL of one cab is 3dB lower than the other, acoustic summing gives you about +4.6dB over the SPL of the loudest cab. For example 90dB and 87dB = ~94.6dB
If the SPL of one cab is 6dB lower than the other, acoustic summing gives you about ~+3.5dB.
If the SPL of one cab is 10dB lower than other, acoustic summing gives you about ~+2.4dB.
We generally assume you need at least a 3dB change to clearly hear a difference. With a 10dB volume differential between the two cabs, you may not notice any benefit from adding the 110.
I used this web calculator for the acoustic summing estimates:
Total dB level adding of coherent correlated sound sources combining decibels or SPL sound pressure level audio logarithmic decibel scale loudspeaker add signal noise levels incoherent noncoherentt - sengpielaudio Sengpiel Berlin