Originally Posted by
rickair7777
I don't think that would be legal because wind could blow you off the desired track and you would have no way of knowing or correcting. Legally you need something that can actually get you there in a straight line...VOR-based RNAV, GPS, or vectors.
I din't mean to give you too much of a ration, just wanted to emphasize the importance of precise IFR procedures. If it makes you feel any better I failed my first CFII oral because I tried to describe a similar technique (for a hypothetical lost comm situation).

Could calculating your heading and using the DME from the GPS not count? You'd know when you were being blown off course because your DME would change. Kinda like an arc? I'm still 99.99% sure illegal but the curiosity wheels are turning.