TL;DR NO, exceptions are usually faster on the non-exceptional path compared to error code handling.
Well, the obvious remark is compared to what ?
Compared to not handling the error, it obviously decrease performance; but is performance worth the lack of correctness ? I would argue it is not, so let us supposed that you meant compared to an error code checked with an if statement.
In this case, it depends. There are multiple mechanisms used to implement exceptions. Actually, they can be implemented with a mechanism so close to an if statement that they end up having the same cost (or slightly higher).
In C++ though, all major compilers (gcc introduced it in 4.x serie, MSVC uses it for 64 bits code) now use the Zero-Cost Exception Model. If you read this technical paper that Need4Sleep linked to, it is listed as the table-driven approach. The idea is that for each point of the program that may throw you register in a side-table some bits and pieces that will allow you to find the right catch clause. Honestly, it is a tad more complicated implementation-wise than the older strategies, however the Zero Cost name is derived by the fact that it is free should no exception be thrown. Contrast this to a branch misprediction on a CPU. On the other hand, when an exception is thrown, then the penalty is huge because the table is stored in a cold zone (so likely requires a round-trip to RAM or worse)… but exceptions are exceptional, right ?
To sum up, with modern C++ compilers exceptions are faster than error codes, at the cost of larger binaries (due to the static tables).
For the sake of exhaustiveness, there is a 3rd alternative: abortion. Instead of propagating an error via either status or exception, it is possible to abort the process instead. This is only suitable in a restricted number of situations, however it optimizes better than either alternative.