Helps to always route your Mid mic into a Left or odd numbered input channel and your Side mic into a Right or even numbered channel, because that's the standard channel assignment for doing so and what mixing software and Mid/Side plugins will use. You can fix that afterwards of course, but easier to get it right from the start.
Yes you can "re-adjust" the Mid/Side balance of a Left/Right recording - to some extent and with a few caveats:
1) The range of re-adjustment becomes more limited. You can't get back what isn't there. For instance- if you were to decode your Mid/Side pair to Left/Right at the input stage prior to recording and set the ratio to 100/0 or 0/100 so you were getting all Mid or all Side in your L/R recording, you cannot re-adjust again later, you'll only have all of one or the other in your Left/Right recording. That's an extreme example, but any matrix setting other than straight 50/50 will sacrifice some signal-to-noise ratio in the lower channel which you can't get back. Not a big issue but something to be aware of.
2) You can re-adjust the Mid/Side ratio of any stereo recording and this is the basis of a number of powerful mastering techniques. However, listen carefully for phasing effects when doing so with non-coincidently mic'd recordings made using spacing between the microphones. That shouldn't be a problem for coincident recordings (X/Y or Mid/Side) if the mics were setup so as to be truly coincident.