No. The SR-22 is a form about a policy. The policy is the insurance. You cannot buy an SR-22 on its own, and adding one does not change what your coverage pays for.
More detail
This distinction matters in practice because of how people shop. A driver who asks for "SR-22 insurance" is really asking for two things at once: a liability policy a carrier is willing to write on a flagged record, and that carrier transmitting a certificate to the state. The first is the expensive part and the part that varies enormously between companies. The second is a small administrative fee, commonly in the range of $15 to $25 one time. Treating them as one product is how drivers end up accepting a bad policy price because they believe the filing is what they are paying for. Price the policy. The filing is a rounding error on top of it.