Yes, leave it connected. Only in the case of super long drives in super hot weather is there really a danger of overcharging while driving the vehicle.
Mount a small inexpensive voltmeter for each battery on the dashboard, and you will likely notice that when the batteries are charged fully, the voltage the regulator allows drops to the mid 13s. It really depends on the vehicle platform how the regulator behaves, and if it does hold 14.8v all day long then disconnecting the house battery is not a bad idea.
While my voltage regulator is in my engine computer, and should be relatively smart, it exhibits strange behavior at times allowing 13.7v maximum when the battery is still low, and other times allows 14.9v when I know the battery is indeed full. Ambient temp plays a part, but better if there were battery temp and alternator temperature sensors so it can take those factors into account, but those are just 2 more sensors that can fail and cause even bigger issues.
The two voltmeters you will find enlightening. I certainly do. While I do have a battery monitor that reads amperage, I cannot see it from the drivers seat, safely. I think about adding a digital ammeter to see what the alternator is producing total, and this number would be a bit different than what my current ammeter reads, as it reads only amperage into or out of the batteries, and does not include what the vehicle's ignition and other stock electrics are consuming.
http://www.amazon.com/Voltmeter-2-5...1428279575&sr=8-10&keywords=digital+voltmeter
I've got two of these on my dashboard, but in green. What is good about these particular is you can calibrate them. They only power up with Key turned on, and the voltage sense wires go right to the (+) terminal on the battery.
Mine were too bright, and I placed two layers of 35% tint over them to mute them a bit, but I wish they were Red instead, I also wish they read to 0.01V instead of 0.1v. I did buy one 2 decimal red voltmeter, however it was not able to be calibrated and almost 0.2v low and remains in my parts bin, unused.
One of the most enlightening things is having both and ammeter and a voltmeter while the alternator is charging the house battery and one is driving.
Since the well wired alternator in most cases can provide everything the depleted battery can accept at the allotted maximum voltage, One can see just how much a battery can accept at such voltages and with increasing experience, can closely estimate as to how charged the battery is.