It is certainly possible to play against the Petrov in this way. Indeed, speaking as someone who played the Petrov for 20 years, I can say that this move would throw me for a bit of a loop...but only for a minute or so. The primary thing to remember about the position above is that it's very likely to transposition into the Ponziani Opening after 3...Nc6. In fact, if I saw this played against me in correspondence chess I would almost certainly transposition here, since the Ponziani is well researched and offers black many routes to equality.
But I might argue that the move order here is better for black than the mainline Ponziani (1 e4 e5 2 Nf3 Nc6 3 c3 Nf6 4 d4), since ...Nxe4 cannot (yet) be met with the complicating d5, driving off the Nc6. So the Petrov player would feel very comfortable with 1 e4 e5 2 Nf3 Nf6 3 c3 Nxe4, which after the likely white replies of either 4 Nxe5 or 4 Qe2 generate positions which the Petrov afficionado will find quite familiar.
That being said, I wonder whether a player who regularly plays the Ponziani might not do well to play 3 c3 when he comes against the Petrov. So in short, I don't think it's bad, but I'm not sure we're breaking any new ground here.
When iwas going through lines of the saragossa opening I noticed something that made me laugh a little at first but then I examined it a bit more and relised (nothing concrete) that it could have some potential check it out.
It plays out like this 1.e4 e5 2. Nf3 Nf6 3. c3!?
Now this looks odd but some continuations are quite good see my blog for more information but post lines here with refutations because I am sure that we can get some success out of this.