Is it OK to do additive smoothing before applying Pearson's chi-square test for independence?

Question

I'm concerned about treating my data as gold, especially in areas of low data support, so I would like to apply additive smoothing. I'm then doing several things with this data, and one of them is Pearson's chi-square test for independence. Is it still acceptable to first do the smoothing and then do the chi-square test? The former is very Bayesian and the latter is very frequentest, so at the least it feels somewhat strange. However, it seems like smoothing should curtail the need to worry much about the data support or the need for something like Fisher's exact test.

My reasoning for wanting to use competing philosophies is because the audience really wants to see p-values, but the Bayesian inside of me is fighting to be let loose. As such I came up with this compromise.

EDIT: To clarify how I envision the smoothing taking place, consider the following contingency table:

    X=0  X=1
   +-------+
Y=0|  2|  2|
   +---+---+
Y=1|  3|  3|
   +---+---+

So without smoothing we have:

$P(X=0)=\frac{5}{10}$, $P(X=1)=\frac{5}{10}$, $P(Y=0)=\frac{4}{10}$, $P(Y=1)=\frac{6}{10}$

With additive smoothing and say $\alpha=1$ we get

$P(X=0)=\frac{6}{12}$, $P(X=1)=\frac{6}{12}$, $P(Y=0)=\frac{5}{12}$, $P(Y=1)=\frac{7}{12}$

I haven't yet decided how to handle the contingency table. One way would be to smooth each cell:

    X=0  X=1
   +-------+
Y=0|  3|  3|
   +---+---+
Y=1|  4|  4|
   +---+---+