A high SWR does not mean that the power isn't being radiated. It does mean that a certain amount of power is being reflected back to the transmitter, but that reflected power doesn't all just disappear - a portion of it gets dissipated as heat in the transmitter final amplifier, but much also gets reflected back out toward the antenna again.
How much actually makes it back out the antenna will depend greatly on the quality of the coax feed line.
I plugged some numbers into a transmission
line calculator. The assumption is that perfectly good RG-8X is the coax feed line, and there is 50 feet of it from transmitter to antenna, and you are transmitting 25 watts at 156 MHz. To get an SWR of 2.9 at the transmitter, the SWR at the antenna has to be about 8:1 in this scenario. Total power loss, a combination of matched loss and SWR loss is 5 dB. That is a power loss of about 17 watts and a power out the antenna of about 8 watts.
(Naturally, if the coax is old and possibly water
logged these number will be much worse. If it is good condition, high quality, low loss coax like RG-8 you would only lose about 10 watts and still have 15 watts out).
Compare all of this to the situation with the new antenna. An SWR of 1.4:1 at the transmitter means (assuming the coax at the beginning of this post) SWR at the antenna is 1.8:1. Coax losses in this setting are almost 10 watts for a power out the antenna of about 15 watts. That is an improvement of about 3 dB over the original numbers with the bad antenna. Not a very big difference at the receiving end.
You could adjust the antenna for a perfect 1:1 SWR and get about 1 more watt out the antenna, but 9 watts is still lost
in the coax.
So sure there will be an improvement. I'm just saying it might not blow his socks off. Hope I didn't glaze everyone's eyes over.....