Does hopping have an advantage?

Hopping helps in multiple ways:

• It's the only way to drift, which allows for sharper turns without losing (too much) speed. Drifting is done by jumping and keeping the jump button pressed while landing at an angle.
• If you can maintain your drift for long enough, you gain a boost upon letting the jump button go. If you keep drifting, you can get a stronger boost. Mario Kart 8 Deluxe offers a third boost level.
  
• Hopping off a ramp or ledge gives you a small boost upon landing. Your character will perform a stunt to let you know you timed your hop properly.
  
• Mario Kart 8 has an exploit named "Fire Hopping", in which a player could hop repeatedly from left to right to get extra speed from a boost. This exploit has been fixed in Mario Kart 8 Deluxe.

While you can easily ignore drifting in 50 CC, it's very helpful for winning 100 CC, and absolutely necessary for 150 CC or higher.

I was wondering if maybe it could also make you go faster if you went off road by accident.

No, but hopping before you get off road helps delaying the loss of speed until after you've landed (if you're landing off road). This is most useful at higher speeds (such as 200 CC), or right before your Mushroom boost runs out (if you're still off road by then).