Short answer is yes.
If the business claims rights to use a mark, they may use the “TM” (trademark) or “SM” (service mark) designation to alert the public to their claim of a “common-law” mark. No registration is necessary to use a “TM” or “SM” symbol and they may continue to use these symbols even if the USPTO refuses to register their mark. Those symbols put people on notice that the business claims rights in the mark, although common law doesn’t give them all the rights and benefits of federal registration.
The business may only use the federal registration symbol “®” after the USPTO actually registers a mark, not while an application is pending.