Yeah, it is doable. I've done it at least a couple of times. Once you leave Arroyo, you need to go to San Francisco and take the quest to get the Vertibird plans in Navarro (where you will find the set of Advanced Power Armour). While travelling the wasteland, you will have to safe very often (travel short distances, like one or two squares at a time and save your game). However, if you have Advanced Power Armour so early in the game, it'll take away a lot of the fun (gunfights will be child's play). You'll also level up way too fast (for instance, the quest to get the Vertibird plans for the Brotherhood of Steel gives you 20000 xp!). If you've never tried it before, it might be fun, though. You'll also be able to get your hands on some very nice weaponry and armour for you and your future NPC's (in the BoS bunker in San Francisco and in Navarro).