While the arguments put forward in the other answers are in principle correct, it is important to note that nuclear decay processes span a huge parameter space, both in energy and half-life.
So to provide a counter example, let us look at the most special nuclear transition in this regard: Thorium 229, which has an isomeric state Thorium 229m, which can be obtained as a decay product of Uranium 233. The transition energy of this state is 8.28 +- 0.17 eV (source). Yes, eV! This transition is in the optical regime.
As a result, it gets affected by all kinds of electronic processes , for example, internal conversion . Also the chemical environment or rather the crystal structure is relevant (as stated here). Note that there is a huge body of literature on this subject and I only give examples here which are by no means representative of the whole work. For further reading see this and references therein.
Note that this is an extremely exotic transition, but also a very important one. Much effort is being invested into building an extremely precise nuclear clock using these nuclei.
So at least a weaker version of the question in the OP can be answered in the affirmative: there are radioactive decay processes that get strongly affected by the electronic environment.
Edit for clarity
I have been asked in the comments to clarify my answer with regards to how it addresses the question and what kind of nuclear transition we are talking about.
- (in response to @Helen's request) My answer points out a particular nuclear transition that is affected by the electronic environment. The transition may be considered exotic, most other nuclear decay processes (especially alpha and beta decay) will not be affected in such a way, as pointed out in the currently accepted answer. Whether this constitutes a "yes"-answer to the question can be debated.
- (in response to @Emilio Pisanty's request) The Thorium transition is a very special gamma transition of an isomeric state that has an untypically low transition energy (see Figure 3 in this open access paper for a nice visualization). Indeed, it is the lowest lying known transition. The excited state may decay also via other decay channels, such as internal conversion, where a shell-electron is ejected instead of the emission of a gamma photon. The mass and charge of the nucleus is not changed in either of these, as usual for a gamma transition.
Also check out @BCS's answer for another nice example that works via electron capture.