I have a towing hitch on the front of my motor-home for this purpose, I also have one on my Nissan Titan for when I'm pulling my travel trailer. Peace of mind when you can see what's falling off!

I'm sure the producers added extra support for this to happen. 

In my opinion, depends on a few things...if you have a classic Mini. If it's a 'modern' MINI (2001-Present), then it's fine. 

Depends on the weight of the bikes. Some are heftier than others. Then to have two of them, that's pushing it. Especially if you're thinking of a roof rack. You'd be maxing out or overloading the weight amount that the gutters rails could handle, depending on the bikes. Then every bump and thump in the road would have that weight be jarring or compromise it even more. 

The other factor would be, what condition are your gutter rails in? If they're old, possibly rusted, bent up or pulled out by previous loads, accidents, etc, then they may not be up for the challenge. 

The e-bikes of my wife and I are about 50lbs each. A 100lbs total of weight on the roof rails (not including the weight of the roof bars, and bike holders) distributed over four points of the roof rack bars sitting on the gutter rails, wouldn't be horrible. It would be close to maxing it out, if not over. Not sure what the official limit is. But even official numbers are usually conservative and over-safe.

To eliminate a bunch of weight, take the batteries out. Most e-bikes have this option. Ours have two big batteries each. One main, and one reserve. Once the batteries are taken out, that's a lot of weight savings on the supports. It makes lifting easier also. But keep them somewhere safe where they aren't going to get banged up, hot or wet. Batteries don't like that. Without the battery weight, the bikes are basically the weight of a manual-pedal bike. Maybe a bit more. Way more do-able for roof transport. 

I asked a bunch of weight-related questions to the Mini community around me that constantly go on long road trips. I have the roof rack bars that are supported by the gutter rails along side the car's roof edge, like seen in the photos. Those can only support so much. There's not much meat there.
There's also a roof rack bar set up that is supported by those gutter rails and suction cup supports in the middle of the bar/basket that push down in the center of the roof. Again, that isn't a good point to support much weight as the roof span isn't supported by cross members under it to support weight. It's just a thin sheet of metal across the entire span. 

If you have a roll cage in the car, that would help support the weight with the batteries left in. The inner bar (inside) that runs across the headliner/roof from one side to the other would help distribute the weight, if the weight was supported over top of that bar from above (outside). 

The folks that do the big road trips have either the basket style roof cargo option, or the roof bars with an enclosed cargo carrier as seen in the photos. Some have the bars with a cargo carrier and a bike rack included. But with a manual pedal bike, not e-bike. Either way, they sometimes have spare wheels/tires, cargo bin with some supplies, luggage, jerry can(s), etc. And even then, they're pushing it or close to it with that much stuff.

If you really want to get wild and confident/safe, I'd run a bead of a weld under the gutter rail to try to support more weight. You'll frig up your paint job a bit along the rail, but can touch it up or re-paint...if you're really adamant about a roof rack for two bikes with the batteries left in. If your Mini is in a state of repair, restoration or repaint anyways, this is a good time to do this. 

Then there's the mentioning of having to hoist the bikes up to the roof in the first place. Which would be cumbersome, awkward, painful, etc, with the batteries left in.

There could be an option to have a bike rack out the back if you have a hitch. There's bike racks for that option. The hitch receiver won't be as thick and hardy as most hitches you see on regular cars, so the weight limit will be less than an average hitch. A classic Mini hitch is pretty skimpy. But this would still be a better solution than the roof option. The hitch would hold the weight more so than the roof. And easier to load and unload the bikes from the hitch level, then the roof level. 

Happy hauling.

A better idea might be to install a suitable bike rack on the motor home above the tow point for the car. Or on the front like municipal buses have. You might also be able to install an electrical outlet to charge the bikes while you camp or drive.

Two questions. Which mini Original or BMW? Have you tried lifting the bike over your head? 

We’re thinking about purchasing a mini to haul behind our motorhome, and are curious if a mini is suitable for a bike rake that can carry 2 heavy e-bikes? Any suggestions?