The Traxxas BEC will work better than no external BEC, but it probably wouldn't be able to supply as much current compared to other UBECs (e.g. CC UBEC). (IMHO) It's best if you don't just limit yourself to plug-and-play modules, but it is your decision.
Unfortunately, Savox servos are also pretty power-hungry, but if you really are avoiding soldering, the Traxxas BEC is worth a try... Traxxas doesn't list the specs of the current supply and other specs for the BEC, which is why I am hesitant to say it works with other servos. If you want to go...
You can technically run the servo (any servo) without a BEC, but under load, it will draw a lot of current (to not stall), which can strain (and maybe damage) the internal BEC (voltage regulator) of the ESC by causing brownouts. The XL-5 HV that comes with the TRX-4s and TRX-6s is only able to...