Does a two pole breaker trip if only one leg is overloaded?

Yes. Both legs do not have to be loaded for the breaker to open. A standard two pole molded case breaker has a common internal trip mechanism, so an overcurrent on either pole trips both poles simultaneously. You do not need 80 percent on both legs, and you do not need the two currents added together to exceed the rating.

How the code describes it

Section 240.15(B) of the 2023 NEC covers circuit breakers as overcurrent devices on grounded systems. Section 240.15(B)(1) permits individual single pole circuit breakers with identified handle ties to protect each ungrounded conductor for line to neutral loads in multiwire branch circuits. Section 240.15(B)(3) permits a single circuit breaker to protect a single phase line to line load on a 3 wire, single phase system that has a grounded neutral, and Section 240.15(B)(4) covers 3 phase line to line loads. In every one of those cases the intent is that a fault or overload on any ungrounded conductor disconnects all the ungrounded conductors of that circuit.

Section 240.6 lists the standard ampere ratings for fuses and inverse time circuit breakers, and the rating on a two pole breaker is the rating per pole. A 30 ampere two pole breaker means 30 amperes on each pole, not 60 amperes total. That is the number one misread of a two pole nameplate.

Common trip versus handle tie

A common trip breaker is a factory assembled multipole device with a single mechanism. Trip either pole and both open. This is what you buy off the shelf as a 2 pole breaker.

A handle tie is a listed accessory that ties two single pole breakers together so the handles move as one. A handle tie gives you simultaneous manual operation and, per 240.15(B)(1), is permitted for multiwire branch circuit disconnection. It does not guarantee that an overload on one pole electrically trips the other pole. It provides common disconnection, not common trip. Section 210.4(B) requires each multiwire branch circuit to have a means that simultaneously disconnects all ungrounded conductors at the point where the circuit originates, and a handle tie satisfies that.

Why a leg still gets hot without tripping

An inverse time breaker follows a time current curve. It will carry its rated current indefinitely and needs meaningful overcurrent for a meaningful time before the thermal element opens. A leg running at 90 or 100 percent of the rating gets warm, the conductor gets warm, terminations get warm, and nothing trips. That is normal breaker behavior, not a defective device. Section 210.20(A) is the sizing rule that keeps continuous loads at or below 80 percent of the breaker rating precisely so that condition is avoided by design.

Field takeaway

Two pole breakers are common trip. One overloaded leg opens both poles. Read the rating as amperes per pole, and if you are combining two single poles to serve a multiwire branch circuit, use a listed handle tie and remember it gives you common disconnection rather than common trip.