There are multiple ways to look at this question, so I'll explain my assumptions and try to answer what I think you mean.
By a radioactive molecule, I'm assuming you mean that the molecule contains an atom which is radioactive (meaning that atom is capable of spontaneously releasing a high energy particle from the nucleus).
There are then two ways to look at your question. First, you may be asking if these radioactive atoms form stable compounds, to which the answer is yes. There are many researchers who study the chemistry of uranium and other radioactive heavy metals. They try to find out what compounds they can make and what they can be used for. Often this research is directed at developing new forms of chemotherapy by getting the high energy radiation source directly into the cancerous site.
Moreover, the entire concept of carbon 14 dating relies on the fact that carbon 14 (the most common radioactive isotope of carbon) behaves nearly identically to carbon 12 and carbon 13 (which are both non-radioactive and much more abundant) in molecules. The fact that organisms incorporate carbon 14 into their constituent molecules is what allows us to determine their age tens of thousands of years later.
However, I think what you are really asking is whether a molecule can stick together when an atom in that molecule undergoes radioactive decay. Basically, does the radioactive event blow up the molecule? The answer here is it depends. What holds a molecule together is the strength of its bonds, and when an atom undergoes radioactive decay it shoots out a high energy particle. From from Newton's third law we know that every action has an equal and opposite reaction. Thus, figuring out whether a molecule will survive a radioactive decay requires figuring out whether the recoil of the nucleus (the reaction to the action of shooting out the high energy particle) is higher in energy than the bonds of the molecule.
The three major types of radioactive decay are:
1) alpha decay - the radioactive element shoots out an alpha particle (which is the same as a helium nucleus). There is zero chance a molecule survives in this situation. The nuclear recoil is much much higher in energy than the bonds
2) beta decay - the radioactive element shoots out a beta particle (a positron or negatron, basically something with the mass of an electron which is thousands of times lighter than an alpha particle). The molecule may survive this but it usually doesn't.
3) gamma decay - the radioactive element shoots out gamma radiation (really really high energy light). The molecule will survive this kind of decay.
Hope this helps.
