Yeah- NEVER use one. Never a problem- but that's with a cruiser frame that has clearance. The modern frames are almost as light as a vintage steel roadframe anyway, and with light wheells theres practically no difference in the roll.
Coaster brakes are PREHISTORIC! Get a freewheel wheel. You'll have to set up brakes then, with a dual lever.
I set the motor chain first- with a derailleur on the pedal side it totally takes away allignment between chain problems, but I've also got another build I matched up without any tensioner- you can use half links- on the pedal side the smaller chain is MUCH easier to split and work with- or you can also sometimes vary the freewheel on the pedal side- single freewheels aren't expensive -BEWARE OF CHEAP CHINESE THAT HAVE NO SLOTS FOR A REMOVER!- Also make sure it is compatable with your chain- if it's 3/32 it will work with either a 1/8" pedal chain or a derailleur chain- but you can't put a derailleur chain on a 1/8 inch sprocket- 3/32 has become more the standard, but they are both still common.
Or you could even have a multi-speed cog set on just one and then maybe vary that-
when you make changes on either side- you have to divide the changes in the teeth by two- because the chain only contacts the back half of the sprockets-
if the change is an even number- once divided by two- it will sit about the same in the chain stay- if it's an odd number, it will move one way or another by half a link- if you want it in the same place, you have to use a half-link with an odd number change. Once you get this concept down you can pretty much predict the results-
also if you are mounting a kit, or putting on a new motor chain- yes it will probably stretch more in relation to the pedal chain- so a little bit more play on the pedal side will disappear when you later pull the chain back in the stay a bit for the stretch- Don't start at the far end! Always try to be in the middle, or just a bit on the near end with a new motor chain. But be careful, a too lose pedal chain could come off, especially with cheap chainwheels.
I like to convert to lightweight well-made three piece alloy cranks- but I have used a low rider 36 sprock on the front, which gives you an easy peddling gear for a bike that's heavy with a motor. You can change steel front sprockets for under $20 if you shop around.
A bike with verticle dropouts will prove difficult without a tensioner or derailleur, but the frame clearances are also a factor- that's why I always use a modern lightweight cruiser.
here's when I still had on the low rider 36 steel sprock with a 22 freewheel on the back- light light gear- not fast but very comfortable in parking lots and pedestrian ways.