As far as I know, no.
The only impact ist that the general will become more loyal to you. This can save your hide from a nasty civil war at times. And should you actually have one, this general is more likely to side with the royalists than the rebels.
Only HRE can have its Emperor elected from among the generals, and then those married with princesses seem to be favoured somehow. For all normal factions, the only general eligible to take over the line is that with a royal blood (i.e one of the members of the family's side branch). While he is a normal general (not a King or Prince), you can marry your princess to him without fear of an incest. Should your line die, he can then take over the country as a powerful, say 6-star, ruler, already married. Sometimes this can make a hillbilly country into a great empire...
Medieval politics is quite funny at times, y'know...