can a convicted felon be registered as an investment advisor if they pass the series 65 exam?

Generally, no. FINRA, the organization that provides registration to broker, prohibits felons from holding registrations (a/k/a layman's terms as a license) - the term is that they become statutorial disqualified.

For example, Article III, Section 3 of FINRA's By-Laws1 provides that no member shall be continued in membership if it becomes subject to disqualification; and that no person shall be associated with a member, continue to be associated with a member, or transfer association to another member if such person is or becomes subject to disqualification. FINRA's authority to deny the registration and/or membership of disqualified persons or members is set forth in Section 15A(g)(2) of the Securities Exchange Act of 1934.

FINRA then includes in that SD definition "all felony criminal convictions for a period of ten years from the date of conviction".

So, if the term is within 10 years, then no.

The other issue is that an RIA (registered investment advisor) may NOT have to take the Series 65 exam, which would depend on state law as to registration of the RIA, being the amount of capital and number of customers.