Which type of RF harvested device is used now?
RF signals will pretty much never be naturally in phase.  Forcing them to be in phase would require some kind of phase detection and adjustable delay that works in your radio frequency band.  That's going to be complicated, and difficult to do at high frequencies.

It would be much easier to convert the received RF to DC, then connect the DC sources in parallel (or in series for that matter.)

I see you asked a related question on the DSP stack exchange.

The most likely reason that those papers just sum the RF is that the received signals are presumed to be completely unrelated to each other so that simply connecting them in parallel would add them all to a sort of "average power." 



Have you had a look at how much energy you could reasonably expect to collect?  I ran through some numbers in this answer to a similar question.

In that answer, I assumed simple dipole antennas with no gain, 5 watts transmit power, 2.4GHz as the transmit frequency, and 1 meter as the distance.  I then used this calculator to estimate the received power.

Given those unrealistically good conditions, the received power was just 0.00049455W.  That's not quite 500 microwatts.  

What ever device you are powering will have to operate at very low power, or collect energy for a long time so that it can do a short task at high power once in a (long) while.