Yes, the data transmission will take 10's mA for the RX & TX combined plus BLE is limited to about 100kbs of raw data (ignoring the packetisation and error handling in the transmitted stream). BLE connects very quickly to its pairing partner, so you need to think about how much data is going to be sent to work out whether pre-processing is needed to keep the battery small. Also small batteries might not last their full capacity since the transmission Current might clamp the battery to 80% of its useful charge since the available current tends to fall towards the end of the Battery (battery size & technology dependent).
Since you've not said what your measuring or what processing is needed, I'll make two suggestions based on the need for continuous comms to the sensor
The MSP430 series can be placed into LPM3 using a 32kHz crystal and use this to keep the SPI port active up to a few kilobaud, so you could continue to take in readings at alow baud rate waking up the MSP430 when the SPI buffer is full and storing the data in external serial Flash. LPM3 draws about 3uA. If you wake up to one of the default DCO settings of 8MHz, then the supply current is ~2mA, but you'll only be in this mode for a few cycles while you store the data. Once you've got sufficent data to carry out the processing simply wake up the MSP430 for a longer period of time.
Use an ARM Cortex based processor. The Freescale Kinetis L series is quite similar to the MSP430 in that it can operate its peripherals in a deep power down modes (uAs), when other Cortex processors have turned off all of their peripherals only leaving the RTC active.
However, all the Cortex processors (Atmel, Infineon, Energy Micro, Freescale, NXP, ST, TI, etc, etc) are seriously affected by ambient temperature and their supply current escalates upwards very quickly in the presence of rising temperature in Low Power modes towards +85C since they are mostly made on a silicon process below 90nm which has extremely high leakage currents (you can see a rise of 20 fold in Current from 25C to 85C in some cases when these micros are in Low Power modes). This is less of an issue when these parts are CPU active mode, but even in these modes some of them go up 3-4 times in Current from 25C to 85C.
The MSP430 doesn't suffer this issue and only changes by a small amount as temp rises since its made on a very low leakage process.
So the route towards a Cortex processor depends on your ambient temp since if its usually around room temp, then they can offer more performance in your product.
Since these are 32-Bit processors you can carry out integer mathematics quite easily and in many cases in one cycle.