Only if the flyback actually blew - it usually fries the HOT and takes out the B+ fuse. If you're replacing it ahead of time, then no, you won't have to change anything else.
To the OP, check the voltage at the power connector going to the monitor, verify you're actually getting power to the monitor. Check both fuses on the monitor chassis. If F901 is blown, then you most definitely need a flyback and a HOT.
Then you shouldn't have any problems doing repairs on something as trivially simple as a G07. It's about as complicated as a TV set, circa 1979 - only without any tuner, demodulation or any RF stuff. It's quite possibly one of the simplest, best documented, most straightforward arcade monitors. It's a single sided board, nice wide large tracks, really easy to solder to and work on. The schematics and manual are readily available for download as a PDF from dozens of places online. Even if you're not well versed in monitors or this kind of electronics, you can read a schematic, so you shouldn't have too much of a problem with it. If you have any desire to learn about arcade monitor repair, start here.
Check the HOT (Horizontal Output Transistor - 2SD870, on the heat sink on the side by the flyback) to see if it's shorted. It's a simple NPN power transistor in a TO-3 case. When the flyback in one of these monitors fails, it draws too much current and destroys this transistor, so when you test it, it'll be shorted. The next thing to fail is the F901 fuse, which is the fuse for the B+ power supply in the monitor. One thing to watch out for - with that fuse open, there isn't any load on the supply, so it won't discharge the filter cap automatically when you power it off. So, if the fuse is blown and you power up the monitor, that big 680uf/200v cap gets charged up but never discharges. When you remove the chassis, be mindful not to touch it's terminals with your fingers, and discharge the cap manually.
-Ian
