Out of the box, no. If you choose to log object, content, etc. changes, it does all of them. The only time it won't is if you write code around it.
There are a few things you could look at though. One would be to create a scheduled task that would look at all the changes that have been logged every XX hours and if that object is of type xxxx.xxxxx then remove it. I'd suggest creating a custom setting that has a semi-colon separated list of class names so you can easily add/remove items from it.
Another thing would be to capture the events BEFORE they write to the database with a global handler and during the update/insert, wrap the statement in a using statement like so:
using (new CMSActionContext { LogSynchronization = false })
{
// do your work here
}
I haven't tested this method but there is a chance you may already be too late.