I do not think any big problem may be there, but after shut down system Internet will keep sending and receiving data as it does always. So by that way your data usage may be increased unnecessary and may be the problem regarding the security of internet.
So, i recommend we should always keep turn off of internet connection when we are not suppose to use.
And before shutting down the system we need to shut down our internet connection, its good for our network security point of view. If its not means it may be used by some other person, who has great skilled knowledge of network they may hack the connection.
"People says 143. I say 444 i.e. Love Your Life"