Yes and no... There aren't alot of hackers sniffing bluetooth signals while driving but it is feasible to notice your signal and connect with it via default password and start hacking your car. Highly unlikely, but it is possible. Also make sure you have a healthy 12v because the OBD2 reader draws power even when car is turned off. Alternatively, on ebay you can find an OBD2 extension cord with a switch build into it for $5... That way you could mount the switch on your dash and hide the OBD2 reader back behind your dash and flip the switch whenever you want to check in on the OBD2 signal.
That can be as simple as using a cheap connector with poorly (or un-) plated pins. I had one like that and it caused no problems for a few years, then got to where it would light up the dash with comm errors simply by being there. Replaced that cable with one I had lying around with the pins plated gold, rock solid, could plug and unplug with the car on, nary a glitch. Not even a glitchlet. Another thing to think about: there is 24 hour power on pin 16 of that port. The later genuine ELM327 chips have a good low-power mode they can be put in so they draw very little power from that pin when not being used. Some of the cheaper knock-off chips ... don't, and those devices will draw more power all the time they are just sitting there. (STN's version is more than just an ELM327 knock-off, and it has a good low-power mode too.) Even using a chip with a good low-power mode, and having firmware on the device that puts it into low-power mode at appropriate times, there is still some extra cost to making the rest of the electronics in the device also consume as little as possible during sleep. Pages 84–86 in the ELM327 datasheet lay out some of the considerations. Naturally, there are going to be some devices that cut corners there, and some that don't.