Yes
The thing which gave his theory of special relativity credence was the fact it can be used to describe all the laws of electromagnetism (in other words, if you assume the magnetic field is the same thing as the electric field, just "length contracted" and "time dialated"). Thus the electromagnetic field equations are the same.
However, you get the EXACT same results by simply adding travel-time into the formula (in other words, assuming the electric field has a time lag to influence anything around it). When you are using Einstein's rules, you must actually ignore this time lag, incredibly enough.
This should be a HUGE red flag for everyone, since we know that signals do in fact take time to travel.
The other thing that Einstein's rules predict are energy, and that there is a "maximum observed velocity" (the speed of light), which we use in our atom smashers and get very good results from (indicating he is correct). But since Einstein's theories are coming from a re-statement of the original laws of electromagnetism, I believe you can re-state things in non-Einsteinian terms and come to the exact same result. (In other words, the result he got to is correct, but perhaps there is another way to get there, just as there was for the laws of electromagnetism).
And as far as his General Reltivity idea, there are two proofs for this:
1) it provides an accurate first-degree approximation for the pertebation of Mercury's orbit
2) satellites apparently experience time at a slower rate than people on Earth (not really sure if this has been proven)
But any other predictions made by this theory have been hilariously wrong. Galaxy rotation, or universe expansion for example. So wrong in fact, the are making up crazy models in which 99% of the universe is unobservable "dark matter" which has no presence in the universe except adding mass to make Einstein's equations work.
Again, I simply wonder if there's another way of looking at things