This depends very much on the type of receptor. Receptors have a minimum of two functional domains, one to sense the signal (whatever that is) and another that interacts with the signal transduction machinery in a conditional manner (depending on signal sensing). We could call them sensor- and signalling-domains.
If the signal is a ligand that binds to the receptor, then receptor overexpression will cause an imbalance, even when ligands are present a lot of spare receptors will be unbound. Whether this has an effect in vivo depends on how the signal is transduced. If ligand-binding triggers signalling, then the effects could be marginal or undetectable. If however the ligand stops the receptor from signalling (i.e. a negative signal transduction pathway), then overexpression could lead to a dominant negative effect. This is interesting because it may help you to map the signal transduction pathway and find interacting partners.
But remember, there are hardly any clean dominant effects, mostly you have semi-dominant effects which are dosage dependent (dependent on expression levels). When you make transgenic plants, you have to test the overexpression by checking the receptor protein levels with a western blot. It means you need antibodies to detect your receptor. Folks will tell you that you can use RT-PCR to check expression and I say that's just a screening tool, you need to work at the protein level if you want to work with overexpressed receptors.