The reason it might just work is that particularly if CPVC pipe components are used, the heat is not all that high. and a Newcomen engine should work best if the steam is barely hot enough to be steam.
The Newcomen engine is actually an atmospheric engine which uses steam to push the air out of the way after which the steam is condensed by a spray of water. Because of this the coolest steam will be the easiest to condense. Since steam at atmospheric pressure occupies about 15000 times as much space as the water it was made from there isn't all that much steam in the engine and everything is getting cooled by the water spray. The Newcomen engine boiler is little more than a teakettle since its function is to produce steam at little over atmospheric pressure. Probably an open end u-tube manometer would provide adequate pressure control. Given that the the cylinder end cap and the piston head are the closest thing to flat in the "steam exposed parts", are relatively large diameter, and exposed to something like 15psi; they plausibly might need some metal reinforcement But the cylinder wall would probably be adequate. The customary pipe glue could be problematic if one wanted to use it for holding warm parts together because it does tend to soften seriously, but so long as those situations are mechanically retained (as opposed to adhesively) the glue would probably be a useful sealant. However since the pressure forces are inward, even that might be overkill.
No part of the boiler or the piping for the steam would likely fair well at temperature, although I would not be too surprised if CPVC could serve given that it is intended for hot water piping. I know that ABS is reputed to be stronger (e.g. preferred for spud guns) but how it fares with heat I am unawares. The obvious attraction of using plastic pipe is that in the sizes needed it is dirt cheap, and the big advantage of the Newcomen engine is that expense of a proper pressurized boiler is essentially eliminated.
I have been toying with this idea, but I figured I ought to first check to see if anyone has already done this so I don't have to start totally from scratch. For that matter if anyone has built a Newcomen engine model, that would probably have a lot to offer.