Pencils are fine even in fairly high oven heat, and many pens will be okay in the low heat required to cure polymer clay too.
Pens have been "covered" with polymer clay a lot in the past, then baked (ink cartridges always removed first). But clayers have found that some plastics will distort or shrink even in those low temps so they avoid pens with those casings. (Metal pens are fine, of course.)
The go-to cheap pens that used to be used for covering with polymer clay were the Bic Round Stics and Papermates (often sold in packs), but Bic is no longer making the *white* Round Stics (see below**). They've substituted *translucent* cases for the white ones now (and perhaps changed other things), and I don't personally know if those plastics also work for heating at polymer clay temps.
You could try a test pen though, just covering with a thin layer of scrap clay and baking as you normally would to see if they're okay. Or you could look online to see more current tutorials for covering polymer clay pens to see which inexpensive pens are being used.
Meanwhile, you might want to check out the page at my polymer clay encyclopedia site about covering pens/pencils/etc with polymer clay, and also about just adding polymer clay doodads or other embellishments onto pens/pencils, etc:
http://glassattic.com/polymer/pens.htm
As for painting a pencil then drying and baking it, I'm assuming you need to bake for some reason...e.g., you want to some bake polymer clay on the pencil after having painted it, and you can't just bake the clay part separately then glue it onto the pencil.
If you're using acrylic paints, in general they can be heated but they are plastics so subject to the same potential maximum-temp problems as other plastics like the pen cases or polymer clay itself. I don't think that 250 F would harm or change most acrylic paints, but 275 F for a longer time *might*. You'd have to do a test with the type of paint you're using, the temperature you're using, and the amount of "protection" if any you're giving your baking item to make sure the temp doesn't get higher on any part of it during any second of heating (there are ways to do help with that***).
** https://ostranderbellepoint.wordpress.com/2013/04/15/eulogy-for-the-white-barreled-round-stic-bic-pen
*** http://glassattic.com/polymer/baking.htm (click on the category "Darkening, Scorching, Burning" which would apply to the clay or anything on it while heating)
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