Yes. Copy elision can change the behavior of your code if your copy constructor (or your move constructor or your destructor) has side effects.
That's the whole point. If it could not change the behavior, there would be no reason to mention it in the standard. Optimizations which don't change behavior are already covered by the as-if rule. (1.9/1) That is:
The semantic descriptions in this International Standard define a parameterized nondeterministic abstract machine. This International Standard places no requirement on the structure of conforming implementations. In particular, they need not copy or emulate the structure of the abstract machine. Rather, conforming implementations are required to emulate (only) the observable behavior of the abstract machine as explained below.
Copy elision is explicitly mentioned in the standard precisely because it potentially violates this rule.