Most definitely could. Here is a simply way to verify if you are getting any broadband RF interference from your transformers. Get a battery powered AM transistor radio. Tune the radio to a station at about 50 yards from the transformer and start walking toward it. If your radio station is getting swamped with noise as you get closer to the transformer, it would be a clear indication of broadband RF interference. At very close distance to the transformer, some interference would probably be normal, depends how well it is shielded.
Got the radio. I set it on AM, around channel 120 was real clear at about 40 to 50 feet away from transformer. Walked right up to it and radio stayed crystal clear. So I guess the transformer is shielded pretty good.