Can I increase the signal strength by combining two radio transmitters with an antenna?
Lets use a contrived example.  Say your transmitters are operating at 10 MHz.  Wavelength at 10 MHz is 30m (meters).  If we assume the two transmitters are phase together correctly, and if the path length (cable) distance from the transmitters to the antenna are different by 15m, this results in a 180 deg phase shift at the antenna between the two signals, which results in 100% cancellation of the signal.
At 10 MHz, obviously, you should be able to match the cable lengths much better than that so theoretically, assuming you combine the two signals correctly at the antenna, you should be able to achieve a 2X (3 dB) increase in output power.
Now let's go up in frequency to 10 GHz (radar territory).  Wavelength at 10 GHz is now 0.02997m, or 1.18in.  At this frequency the path lengths (assuming everything else is equal) needs to be matched to within a couple of tenths of an inch for the combining to work.  If they differ by ~0.6 in, then the two signals will again cancel at the antenna due to the 180 deg phase difference between the two signals.
Note that in the RF/microwave world, it is very common to parallel amplifiers to achieve the needed power output.  But a great deal of care is taken to assure that the signals combine in phase, which includes identical amplifiers and careful attention to the path lengths and the combiner.