And, the answer is YES. But... (always there is a "but")
Yes, there always is a "but..." because, if you have been around enough, you will know that there always is a trade off.
As some have noted, the Rds of the the IRF520 is approximately half that of the IRF510. That improvement will not come without a price and that price is speed - the input and output capacitance is approximately double that of the IRF510 and it is slower as a result. That may or may not affect you.
Similarly, the IRF620 has a slightly higher Rds than the IRF510 and IRF520, but it can sustain twice the Vds of the IRF510 and IRF520 and that trade off means that the input and output capacitances increase (thus it is slower), but not to the same degree as the IRF520. That may or may not affect you.
Now from the "more than you wanted to know" department:
I have not decapped any of these to look at the insides but I'm fairly comfortable in saying that these probably share a common die layout and they just make metal mask or wirebonding options to add or subtract elements. The doubling of the Vds probably means that they just stack the equivalent of two IRF510s in series into the same package (essentially), thus doubling the sustaining voltage. Similarly, to halve the Rds, they essentially parallel two IRF510s but that of course means that the input and output capacitances double. This is the trade off I spoke of. There is no such thing as a "free lunch" in this sort of configuration.
Why would they do it this way? It's cheaper to manufacture in this manner and you cut product development costs by essentially spawning multiple products from one common element. There are customers that want more Vds capability than the IRF510, there are others that need more current capability than the IRF510; this gives them the option of addressing all those markets with less engineering activity.