For most civil matters the answer is "no". Small claims court is special since there are restrictions on using attorneys, and in that context, it depends on the rules. In Indiana, the answer in their manual is no
Small Claims Rule 8 allows a person to appear at trial and, if he or
she chooses, represent himself or herself and avoid the cost of hiring
an attorney. However, a person is allowed to hire an attorney and have
the attorney appear with him or her at the trial. A person who has
power of attorney for another person may not represent that person in
"Have the attorney appear with him or her at the trial" is pretty unclear, since it doesn't say whether the attorney can represent them. Rule 8(C)(1) states that "A natural person may appear pro se or by counsel in any small claims proceeding", which clarifies that they don't just mean "have at your side". In Minnesota, the answer is more emphatic "no":
A power of attorney does not authorize a nonlawyer to file a claim, appear, or in any other way “represent” a natural person in
As for allowing attorneys in small claims court,
Attorneys are only allowed to represent parties in conciliation court
with permission of the court
(emphasis added). The situation in California is somewhat of a hybrid, but as I read it, it means that the incapacitated person is out of luck, which strikes me as surprising. They say
Self-representation is usually required. There are, however, several
exceptions to this general rule: If the court determines that a party
is unable to properly present his or her claim or defense for any
reason, the court may allow another individual to assist that party.
The individual who helps you can only provide assistance—the
individual’s participation in court cannot amount to legal
representation, and the person can’t be an attorney.
So this is most unlike Indiana is that you can't have an attorney, and all the person can do is "assist". So unless they just waive the rules, this means that if the individual is incapacitated, they cannot have recourse to small claims court.