Will my state accept my notarized document?

Yes. Notarizations done online are accepted in all 50 states and US territories.

For example, Florida Statutes 117.295 states that an online notary, physically located in Florida, may notarize a document regardless of whether the principal or any witnesses are physically located in the state at the time of notarization. 

Under the Full Faith and Credit Clause of the US Constitution, full faith and credit shall be given in each state to the public acts, records and judicial proceedings of every other state. This means that each State shall recognize as having the same effect under its laws as if performed by a notary public of such State any notarization performed by a notary public commissioned under the laws of any other state.