Hi Jack,
I think you would have more issue with the db if you were going the other way because the fields would not be there.
But since you are going from a lower version to a newer version then you may be ok. You may run into some empty fields on the receiving end which could cause an issue.
You can take a look at the 1.8.3 update folder and go thru each folder inside since your version and look for any changes that might cause issues. It is always better to let the system do the update. I would have just installed the same version and then let the system do the update for me..
However since you already have it installed the only thing to do now is try it. If it blows up then share the error here and we will try to help you figure it out.
One issue that might raise its ugly head is if they added any new fields to the middle of the field list rather than the end, if so you may have issues. If they added all the fields to the end of the list then youll probably be ok unless any of those are NOT NULL
Just make sure you have php 5.5 because the new version requires it. And check it by user phpinfo()