Well generally, the 10xx steels have a min/max range of carbon that tends to vary by the steel maker. 1095's acceptable range is 0.90-​1.03% Carbon, so the median is more or less .95% hence the naming. 1020 would therefore be only ~.20% and would be as tough (but also as incapable of taking a keen, hardened edge) as iron. That said, the thought of a tomahawk being made of 1020 scared me at first so I checked out the website and saw that they "start with a strap of 1020 steel and wrap around a full insert piece of 1095 high carbon steel" which is a pretty good, proven method that yields a nice hard edge and soft back.
Anyways, to answer the OP's question:
wooden or plastic pegs, sure. Metal pegs a definite no-no. Unhardened 1020 would be pretty dang soft, and the fact that the hawk is poll-less design gives you a very unsatisfactory shape for hammering and no metal as a "buffer" before effecting the eye itself.
But hey, you're bringing along a hawk and presumably a knife - making tent pegs out of branches is enjoyable :thumbup: