Are you more likely to find a monster in a cave during the day?

Monsters spawn in low light levels only. If the area is above light level 7 monsters will not spawn. Any areas below that level (even down to 1 square) is a valid spawning space for hostile mobs.

When exploring caves, the tunnels you are exploring might not be the only areas within range to create valid spawning spaces.

Mobs can spawn anywhere between 24 and 128 blocks from the player (outside of this range, they instantly despawn). So if you are exploring caves, there is a likely chance that mobs will spawn in another branch of the cave that you are not currently in.

So, to answer your question - Yes, you are more likely to find hostile mobs in caves during the day, but it does not guarantee any specific encounters.