A heavy frigate could not always outrun a ship of the line

Could a Constitution-style heavy frigate reliably outrun fourth and third rates?

No; it might outrun a fouled ship, but weather, water, copper condition, sails, and crew could make a well-kept ship of the line equally fast or faster.

Some third and fourth rates were fast ships with large sail plans. A heavy frigate might escape an opponent whose hull had fouled during a long deployment, but a freshly coppered line-of-battle ship with good sails and an experienced crew could remain faster in the relevant conditions. Tactical classification therefore did not guarantee a safe speed margin.