It can work, but the conversion gets messy. You're going from AC to DC with the converter and then back to AC in the amp. There are a number of car amps that can have some EXCELLENT quality to them, and there are a lot that are absolute garbage. These will have ratings that many of us that are into car audio call "When lighting strikes" meaning they will only make that much power if lighting strikes. This is not the only value that manufacturers might fudge either. I'd have to know what this amp is to be able to tell if it is good or not, but rest assured that car audio amps can be quite good.

With the RCA signal, I think it should be ok as car amps are adjustable and all of them can take from under 1V to several volts of signal strength, depending on the model. The low end tends to be from say 0.2-0.5 V to a higher end of 2.5V-15V. There is no way to correlate better quality to voltage ratings. I know of good amps that are on both ends of that.

I've looked into power inverters more which switch DC power to AC. Those will run from a couple hundred to $600-700 or so depending on how stable you need the power to be and how much power you need. The power converter might be cheaper than that, iirc, but you're not going to pick up a new one of anything approaching decent quality for like $30-40.

Now for the converter output amperage, you will need around 30 amps of output to be able to play 400 watts, depending on the output voltage. If it's an AB amp, then double that value (60 amps)as AB amps are about 50% efficient. If it's class D then figure around 43 amps as they are about 70% efficient on average. Since it's for mids and highs, then the first one sounds more accurate as next to all of those are AB amps.

I can't give any recommendations as to which power converter to use as I just don't know. theendofday can use Google just as well as I can (I would hope ) to find a place that sells them. Maybe link them back here and see if anyone finds something suspicious. You want to go from AC power (the wall socket) to DC power (what the amps takes). When searching, don't confuse this with a power inverter which goes from DC to AC. It wouldn't hurt a local audio shop what they use in there demo boards as it should be of appropriate size for what you want, especially if you've dealt with them before. The worst they'll do is not tell you.