To a degree this was tested on the night of July 2, 3 by the PBY call sign 62C attempting to reach Howland from Honolulu. 62C was on 4235kc and Itasca on 355kc. I am sure 355 was CW, morse code, I expect 4235 was also cw. Thompson reported good hourly communication all night with 62C. So, on different frequencies with different operators at least on 62Cs end, using a different mode and presumably the aircraft using a trailing wire antenna communication worked fine.
This DX padition will likely "prove" the same thing.