Yes the amp can be run from what ever head unit you currently have as it accepts a high level input (which is tapping into the signal from the speaker wires). Or if the stock unit has RCA preouts then those can be used.
Another option is using a unit like a 3sixty.3 or the likes, to run the amp.
i personally would suggest using a monoblock amp to run the subs. This will allow you more wiring options as the amp will likely be stable at 1, 2 and 4ohm loads.
Going off the RMS of the amp you stated, the subs will be way under powered also.
Yes the amp will work with the subs put simply, but there are better options.
Also using that amp to wire the subs will mean if the musics bass tones are not centred then one sub will pump harder than the other because each sub will have to be wired to the right channel and the left channel independently.
Subs 2ohm coils, wired in series to 4ohm will see 170WRMS each from that amp.
Both subs can't be wired to a 4ohm load which is stable for bridging on that amp, which is why i suggested a monoblock amp (or you could use 4 channel amp and bridge front and rear outputs).
I hope that helps a bit, even though i have wafted on a bit. Can't simplify all my thoughts at the moment....too late at night for me haha