That would be acceptable to me, but probably more information than you need to give.
If you have a transponder, we'll give you a squawk code (and perhaps ask for an ident as well) and radar identify you that way. We will then call "radar contact" and advise where we think you are ("two-eight miles northwest of Podunk VOR"). If you don't have DME you won't be able to cross-check the milage but you can at least confirm you're on the 340-ish radial and be confident the controller knows exactly where you are.
In this situation the position report is useful so the controller starts scanning the appropriate area of the scope. If you're in an area where sectors are relatively small, e.g. in the terminal (TRACON) environment below 10000 feet or so, there aren't a lot of places you could be and an exact position report isn't crucial. Even if you don't have DME, you can look on your map and see that if you're on these two intersecting radials then you're in an area approximately twenty to thirty miles northeast of Podunk and you tell us that—and that's fine. If you're calling a center controller whose sector might be upwards of a hundred miles or more in either direction, the position report becomes more important.
For this method, if you think you're near to a named intersection/waypoint, giving a position relative to the waypoint is just as good as giving it relative to a VOR. Well, probably just as good. Depending on how well the controller has their airspace memorized.
If you don't have a transponder, an accurate position report is one way of establishing radar identification. In conjunction with the report you also need to tell us your heading or route of flight. We look and see if there is a single target in that area on that heading and radar identify you that way. If you don't give us either piece of information, or if there are multiple possible targets, we can issue an "identifying turn" of thirty degrees or more and observe a single target make such a turn and thereby identify you.
For this method you would probably want to be pretty close to a defined waypoint in order for it to be useful to identify you based on position report alone. Say within a mile or three, for a TRACON controller. A center controller will be zoomed out more; if you're the only target in the vicinity you might get away with five or ten miles, maybe.
For your information, at least in the terminal environment, there is a command we can enter to draw a range-and-bearing line on the scope from any target, or from a defined VOR or intersection, or from any clicked-on location, to any other target/fix/location. If you give a position as the intersection of two radials we would be able to draw those radials on the scope and see where they intersect. But that might be more work than a controller is willing to do unless they're having a really hard time finding you.