I assume that people would prefer to have foreign currency to no tip. But should I absolutely make it a point to covert some currency first thing so that I can tip in Pesos?
In general I would always arrive in a country with a least a little local currency (if it's legal to do so, which it isn't always but is in the Philippines). There's been a couple of times I've been close to stranded on arrival because I didn't. You probably need money to get from the airport (unless you've pre-arranged transport), and exchanging money in the airport isn't the best deal (plus the counters aren't always manned).
In Manila airport there are ATMs just outside customs that will take international cards.
You can certainly tip dollars, be aware that people will probably getting a very poor exchange rate for them. You'll need to pay transport in pesos. Try and have some smaller bills if at all possible, taxis (airport taxis in particular) will often claim to have no change to force you to pay them 1000 pesos for the trip. ATMs will dispense down to 100 peso notes if you request an amount they can't make in larger notes.