Not necessarily antennas. Antennas are in physical layer, not transport or network layer. 802.11n can have multiple antennas but if you are at the boundary of the coverage, multiple antennas won't help much. Multi-path TCP is more about multiple transport streams. Of course it would require separate antennas for Wi-Fi and 4G but that's already the case on current mobile devices. So nothing changes in this sense. It won't affect battery life much from aspect of antenna power consumption because you can only set 4G to backup link, and MPTCP won't offload to 4G until Wi-Fi is not responsive. If you are using full MPTCP (using two links all the time), then that's the tradeoff between performance and power consumption.

In my experience a data link takes far more power than wifi, so the extra use won't be very notable.

I think that the opposite is true (but depends on the type of connection). Mobile stations are focused on low power, they were designed that way from the beginning (e.g. they constantly try to reduce the transmit power if you have "too good" reception so it will be just good and use a lot less power) unlike wifi.

I remember the first mobile prototypes that were used around Motorola were dying of battery after few hours if used wifi instead of mobile data (that was about 8 years ago - so probably we are talking GPRS here).

That's not exactly how this works; you can just maintain simultaneous connections over both network methods. This consumes a very small amount of data on both, but will intelligently shift the bulk of data between the two as connectivity/packet loss/etc changes. It's about being able to seamlessly go from one to the other and back again without having to halt and re-open TCP connections every time, not about using both connections full-out all the time.

Checkout the tech talk if you want to know more.

Bugs have antennae, radios have antennas (or aerials).