It's definitely possible. I don't know if you have one of those portable shortwave receivers, but if you do, you could check the amateur bands with that and see the interference. Generally, you're gonna get more interference on lower bands such as 160, 80, and possibly 40. Then you will on the upper bands like 20, 15, 12, and 10.
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In addition to what @shortwavesurfer has, I would like to add you go through your house and look for noise inside. I found many noisy electronic devices when I did. I suspect you are more likely to find interferences this way. The call is often coming from inside the house.
I have an OCFD which has the long leg within ~20ft of the neighborhood lines but the don't cross. I don't hear any noise but it is at about a 45° angle to the lines. I have a "kinda ugly" common mode choke I built and put up with the antenna so I can't tell you if it's choking out noise but I would suggest you use one. If you hear interference, you should contract your power company and let them know because the lines aren't supposed to be interfering (at least in the US).
Depending on your geometry and distance between your antenna and the power lines, there may be impacts on your reception and transmission. I don't know enough about thee physics, though.