All below-waterline toilets need INTAKE vented loop
It has nothing to do with overboard discharge, it breaks the siphon in the flush water INTAKE line started by priming the toilet pump. It also keeps the bowl from filling up with water and overflowing if the toilet is left in the "wet" mode. It's the most common cause of boats sinking in their slips.
Even though a loop in the toilet DISCHARGE line isn't necessary if you're only flushing into the holding tank, a loop can be very useful if it's an uphill run to the tank...'cuz if it's mounted immediately after the toilet, higher than the tank, the toilet only has to push bowl contents over the top of the loop...gravity will get it the rest of the way to the tank. A loop in the discharge line can also prevent waste in the tank from running back into the toilet when the boat is heeled.
You can't put either one under the sink...that's not high enough...loops MUST be at least 6-8" above waterline AT ANY ANGLE OF HEEL...which is about 3' above the toilet. So they have to be mounted on the bulkhead. It'll prob'ly--to you anyway--look like a mess behind and above the toilet. (See attached photo...the small one is the intake loop, the large one is the discharge line) But it's a BOAT...it's not just a floating condo! Condo's don't need protection from sinking...boats do! If decor is that important to you, you can always cover the loops with a nice teak or mahogany box...or, if there's a hanging locker behind the toilet, you can run the hoses through the bulkhead and put 'em in there. Just be sure that the loops remain accessible for service--cleaning and/or replacement of air valve.