It's [possible, not really desirable.
If you think in terms of channels, it will help. 4+1 is 5, regardless if you use two 2-channel amps, and a monoblock or 1 4-channel and a momnoblock or 5 monoblocks, 5 channels any way you slice it.
I know that seems obvious, but I make this distinction for a reason,
If you split the initial signal to all 5 channels, all your volume control is based firstly on the single speaker leads providing the signal.
This means that you have to tune all the gains, every channel, to set the front/Rear, Right/Left as you like it, ahead of time, because you will not be able to adjust anything but R/L, no front-to-back fader at all.
Ideally, you want a 6-8 channel source you can adjust at your fingertips.
Now there are some multi-channel LOC's that have Bluetooth you can control from an app, or some that have a wired remote.
The best case scenario when you are using the factory head unit is to utilize front and rear sets of speaker leads so you have front to rear and side to side balance controls.
This would require two LOCs or one multi-channel LOC.
No need to get a 5-channel if you have the monoblock already; adding a 4-channel would be the same as having a 5-channel.
As for the Recoil 4-channel amp, consider spending $10 more and get the DI800-4. Set the gains conservatively; it will give you lots more power without breaking a sweat.
My rule of thumb is RMS plus 50%, and in your situation, the 800-4 is a no-brainer.
Here's a good buy for a LOC.
Another excellent option:
At the end of the day, you can split the signal off the 2-ch LOC 5-6 ways; you just have to tune everything for balance ahead of time.