Ground fault causing main breaker to trip
Probably Not
Note: US-centric. Basic principles apply elsewhere but due to different implementation (e.g., whole-house RCD), this may not be the case in some places around the world.
The key is that ground fault and regular breaker trip are two very different things.
Regular Breaker
The basic premise of a regular circuit breaker, whether a main breaker for the feed into a panel (typically between 60A and 200A), a circuit breaker for in the panel for an individual circuit (typically between 15A and 40A) or a circuit breaker built into a device (e.g., a surge protector - not the GFCI type in a hair dryer) is monitoring the total current flowing through on the hot wire to see if it is over the limit.
A regular breaker will trip in two modes:

A lot of current hot to neutral
A lot of current hot to ground (&quot;ground wire&quot;, not &quot;the earth beneath your feet&quot; - because it is very unlikely to get a lot of current flowing through you to the earth beneath your feet because you are not a great conductor. Well, maybe if you were Leonard Bernstein.)

A regular breaker will not trip if there is a normal amount of current, even if it is enough to kill an elephant. Or a herd of elephants.
The dramatic quick trip (within 2 seconds of a problem) is from a short-circuit or a near-short-circuit. Examples include turning on a breaker after replacing a receptacle or switch with a bare ground wire touching a hot screw, animals chewing through a cable (hot exposed touching either neutral also exposed or ground or metal conduit), certain modes of receptacle, switch or appliance failure, etc. Technically speaking, in these cases it is possible for any breaker in the sequence (e.g., both the branch circuit and the main feed) to trip. Generally speaking, if the branch circuit is small (e.g., 20A) compared to the main feed (e.g., 100A), the branch circuit will trip first, providing protection to the affected circuit without turning everything else off.
Ground Fault Circuit Interrupter - GFCI
A GFCI doesn't look at the total amount of current. It looks at the difference between the hot and neutral or (on a US 240V circuit) between the hot wires. The idea is that all current should go into the hot &amp; neutral wires and no place else. That &quot;else&quot; is &quot;ground&quot;. Ground in this instance does not necessarily mean the ground wire. It can mean the earth between your feet. A GFCI does not trip (except if it burns up, but that's not the same) simply because a lot of current flows through it.
A GFCI is primarily for life safety. A small amount of current is enough to kill an elephant - or a person - if the current goes through the heart. One hand on a hot wire, the other hand in a sink full of water, and you've had it. It doesn't take a lot of current (so it doesn't trip the regular breaker) and it doesn't take a lot of time. GFCIs act very fast and with a very low differential in current.
A GFCI will trip in a few modes (using hot/neutral 120V as an example, but similar for 240V):

Current leaks from hot to ground wire. Now hot &lt; neutral.
Current leaks from neutral to ground wire. Now neutral &lt; hot.
A person or animal touches a hot wire - current leaks from hot through person to the physical earth. Now hot &lt; neutral.

The first of these would also cause a regular breaker (circuit or main) to trip. But it will only do so if the total current is large. That happens if there is a real short circuit. Anything short of a real short circuit (where the regular breaker will do the job just fine and the GFCI isn't needed) and the GFCI will catch it and the regular breaker won't.
A GFCI will not trip if all the current in the hot wire matches the neutral wire. Stand totally insulated (thick rubber shoes) and touch one hand to hot and one to neutral and GFCI will not activate. Thanks to the resistance of your body, your regular breaker  won't activate. When someone comes over to your spasming body and touches you, then the GFCI will activate, saving them but probably too late for you (do not try this at home!).
The end result is: Regular breakers (circuit or main) catch a different type of problem than GFCI. Both are important for safety. They are complementary, not redundant.