Well, you don't have to conduct preprocessing and statistical analysis with the same software package, but reviewers might prefer people to rely on just one of those for consistency reasons.
Concerning motion/realignment parameters, you should have an output from MCFLIRT then (if the option to write out the file was turned on), which could be used for SPM (possibly you have to convert the output into a different format though). Motion parameters would be added during the model specification step.
Whether or not to add motion parameters to the design is a topic on its own. The usual motion algorithms are not able to completely remove related artefacts (plus they might introduce some due to interpolation), so preprocessed data will still include lots of variance related to motion. There are many papers on how to reduce its impact, e.g. add the 6 realignment parameters, additionally add their derivatives, ... , add a global motion parameter, also include dummy regressors for all those volumes with fast head motion, ... , turn to more sophisticated methods like ICA to detect and remove motion components.
Best
Helmut
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