Is it possible to complete Moonlit Grotto without using the teleporter in the midboss room?

Yes, it's possible to beat the dungeon without making use of the mini-boss teleport. It's actually faster to not make use of the teleport. The way you're supposed to get around it is to just take the same route you would use to get to the boss room, and then push the block directly across from the room. This will take you back to the mini-boss room, and allow you to get to the blocker from the North with the arrows taking you to the east.

The route to get you through is:

• Start in the mini-boss room
• Walk south to the bumper, which will move to the left and take you to the room west of the bumper room.
• Enter the room to the North, and continue proceeding North until you hit the room with the boss door (you'll need to make use of your seed shooter along the way)
• Push the block directly across from the boss room door, and go through the new opening. Proceed down the southern path on this side of the room.
• Proceed to the the East, which will return you to the mini-boss room. Once here simply proceed South to the bumper room again and it will take you to the Eastern room.

I've edited a map of the dungeon from Neoseeker showing you the route. I had to switch to a white zig-zaggy line part-way through in order to differentiate the from the initial path you take upon leaving the mini-boss room.