No, it wouldn't. If you draw more than you recharge you're eventually going to kill your battery. A battery is a storage bank, and an alternator charges.
So if we take 3700watts total:
3700w / .8 (for 80% amp efficiency, which is a rough average, but you can find yours) = 4625w draw.
4625/ 14.4 voltage (The standard running voltage, but newer vehicles aren't always standard) = 321 amp draw.
That's just the stereo (in addition to what the vehicle uses). This is at full voltage when the bass hits. In between those it's drawing a lot less, and usually recharging. Rock and country has a lot more recharge time compared to rap and techno/house/bass tracks. So that's something that is always relative when figuring out what you need. Plus your vehicle is designed to have a bit more than it's full need: ac, EFI, headlights, brakelights, horn, chargers, ECM, etc.. I would personally be looking for something 300-350 amps, 400 if you can even find it.
Now if you absolutely can't find an alt over 300, then what a second battery would do is give you more time, before you needed to turn your stereo down, and let it recharge.
An isolator is going to separate (isolate) the batteries so they are used one at a time. Most people who use them, do so because they have one battery they plan to use till it dies, and want to have a reserve battery. Most audio systems don't use em, because you are only using one at a time, and in relation to a large system, your vehicle doesn't use all that much power, so you might as well get one large battery or similar batteries and wire them together.
Also know, that when you go alt shopping, there's 3 numbers that matter, and two of them aren't price. Amp output at/or near idle, and RPM for full output. Not sure what your options are, but a good alt will do full output around 2K rpm, and most at idle. A cheap
ebay alt won't do full output until over 3K rpm, and will do less at idle than your stock alt, (where do you cruise at)? That's the difference between a $200 alt and a $600 alt. Some places can even give you an actual curve. If they can't or won't give you those two numbers, then move on.