Whenever I tell people that I Pyrograph on paper, they are usually skeptical at the possible outcome. The thought of the paper bursting into flames is possibly their foremost concern.
Yes it would be a possibility if plain paper is used, plain paper pyrographs poorly in any case. I've tried most kinds of paper and only a few give reasonable results.

The "paper" that is most suitable for use in Pyrography is a bit more complex than the generic variety.

These papers are usually high in cotton content and are made for the rigors of watercolor or wet media usage.

They are rated by their "hardness" which is termed GSM or Grams per Square Metre. I like to use papers that are 200 GSM or higher. These are usually available in a variety of surfaces, from rough to smooth.

Matting boards, used in picture framing, are also quite good to Pyrograph on and are available in various colors.