I've used spay starch (of several different brands) on things on my ironing board for years and years and never had a problem with anything getting sticky, either what I was spraying, or what was over sprayed, or under the board. I have a hardwood floor where my ironing board is located. I sweep and wash the floor and find nothing untoward under the ironing board (well, a lot of thread pieces!).
If you pour a bottle of liquid starch over your carpet it would get hard-- because I've made doilies into lace bowls using the liquid starch. (Soak a doily in liquid starch, then drape it over an upside down bowl-- when dry, remove, and the doily will be in a hard shape the same as the bowl. You can also do this project using a highly concentrated dissolved sugar and water solution.) Perhaps your question arises from the idea of what liquid starch can do in comparison to what spray starch can do...