Yes you'll be ok if you use a 120V transformer as long as you use a 120V balast to power the tubes too, and you might have to change the tube circuit to suit your ballast it should come with a manual that should give you the correct circuit.
Warning!
The tubes used in this project emmit the wrong wavelength to be usefull for developing PCBs. The G15T8 tube emmits UVC radiation at 253.7nm (which is also very harmful to your eyes and skin) this is great for erasing EPROMS and killing germs but it's not good for exposing PCBs.
For this you need a blacklight which has a peak emmision of 365nm in the UVA part of the UV spectrum and is fairly safe. These tubes are either dark violet/black or white when unlit, the white ones should emmit a sky blue colour and the violet/black ones emmit a deep violet/blue colour when lit. The germicidal one used in this project is made of quatz and is transparent so has no phosphor on it. A blacklight has a special phosphor coating that converts the UVC in to UVA.
In general it's ok to use the tubes form insect killers or those violet ones seen in clubs that make your clothes glow. Avoid any un-coloured transparent or rock hunting tubes (these will apear violet when lit and unlit but will be transparent and won't make white paper glow). A UVA tube will be marked BL or BLB so a BL15T8 or F15BLB-T8 will be perfect for this project.
UVC is not very good because it will be absorbed by the traceing paper or transparent plastic film you place the artwork on, it is also blocked by glass and most plastics. It will work to some extent as the UVC lamps do emmit some UVA radiation but it will be no where near as good or safe as UVA lamps.