Bluetooth module as MCU?
All bluetooth modules will need some sort of mcu to handle the requirements of the protocol stack, and it seems common that there will be at least a couple of GPIO which can be used directly if your sensor requirements are simple. At the other end of the spectrum, you will find there are also mcus with a full set of peripherals - enough to support a couple of sensors and a small display for example. Remember, the wearables market is likely bigger than the hobby electronics market.

Limitations are most likely to be in the area of ease of use (as you hint at with your question), and possibly the toolchain which you would need to use (unlikely to be arduino compatible). Also, the bluetooth stack typically takes a reasonable proportion of these wearables focused devices, so there is not a big amount of ram/flash or CPU cycles to spare even if you opt for a part which is more than 'just' a serial-to-bluetooth bridge.