Nothing wrong with Rhumb line Tracks, they worked well for centuries
To address the original question, ABSOLUTELY NO, maintaining the initial Heading will get you nowhere (or at least to the wrong place). Magnetic Variation constantly changes, and even in a nil wind no drift situation, Heading will have to be constantly changed.
Of Course, if you have the facility to fly TRUE Tracks and/or Headings, it would be a piece of cake!
Regards,
Old Smokey