Shveta -

Imputing within categories would help make nonignorable nonresponse, more "ignorable;" that is, you would account better for the mechanism of nonresponse.   If you are having a "significance" 'problem,' please note that p-values are sample size dependent, and your smaller sample sizes by category, if I understand your problem correctly, is what is giving you bigger p-values.   That is why you need to pay attention to effect size, or a type II error analysis, and not set the same "significance" threshold for every case.  (Note that confidence intervals and prediction intervals are less open to serious misinterpretation.) 

Please see the following:

Press release for the American Statistical Association:

http://www.amstat.org/newsroom/pressreleases/P-ValueStatement.pdf

My letter in The American Statistician:   

 https://www.researchgate.net/publication/262971440_Practical_Interpretation_of_Hypothesis_Tests_-_letter_to_the_editor_-_TAS

Hope I did not misunderstand your question.

Cheers - Jim

PS - Actually, however, even though you are using multiple imputation to avoid artificially reducing variance, it still depends on the original data, so the standard errors you estimate for the above should not include imputed data, as that would still artificially increase the sample size.  Breaking up by categories is good.  That helps with "representativeness," but too much missing data is still a problem.   -   If you are imputing in the case of multiple independent variables and have missing data that varies in the number and/or identity of missing cases, and doing multiple imputation on each, so that sometimes for a given "i" you have one regressor, but not another, you might look at the prediction interval with and without imputed regressors, to get bounds on the 'true' prediction interval for each category.  That's what I think I'd do with ordinary or weighted least squares regression.  I suppose analogously with logistic regression, with which I have not worked, however.  

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