Any benefit to low dose radiation?
This is an interesting - and highly debated question. Generally there are two completely different directions of thinking when talking about dangerous substances (this applies to dangerous chemicals as well): 


The linear no-threshold model (LNT).
The hormesis model, in our case the model of radiation
hormesis.


Summarizing the models the LNT model says that every dose has a negative response, so there is nothing like a stimulating dose and exposure should be avoided at any means. This reflects the policy in the handling of radioactive substances. If you look at the figure below, the curves a + b (supra-linear and linear) reflect the LNT model (the figure comes from here):



The radiation hormesis model says that there is a dose range in which the radiation above the background level is not only not harmful, but beneficial. High doses are (in line with the LNT model) also considered harmful. This can be seen in the curves c (linear-quadratic) and d (hormesis) in the figure above. The benefits are thought to take place through the activation of repair mechanisms (which are only activated by radiation) which protect against changes in the genome and thus also protect, once activated, against changes which are caused by other agents and reasons. See reference 1 for more details about radiation hormesis.

There are a number of studies which observe this effects in the laboratory and this is also one of the major critic points: To my knowledge it is currently unknown if these effects can also be seen outside a controlled laboratory environment. 

Other critique points are low study publications (which makes studies prone to statistical errors), using wrong models (cell culture) or too high doses. See references 2 and 3.

Since our environment contains naturally radioactive substances as well as cosmic and UV radiation, we have developed pretty efficient mechanisms to deal with these problem. Additionally measurable effect of radiation on the activity repair mechanisms can be seen (and this is not debated at all), but the main question is if these effects can also have a beneficial effect. It is also not known, if all radiation ($\alpha, \beta$ and $\gamma$) have the same effect, or if some of these like $\alpha$-radiation is more dangerous. 

So I think it may be possible that there is some positive effect, but until this is proven, I would rather be safe than sorry.

References:


Evidence for beneficial low level radiation effects and radiation
hormesis.
Uncertainties in studies of low statistical power
Health Risks from Exposure to Low Levels of Ionizing Radiation