Did we figure it out yet?

If not I will reiterate. Sound meter app + streamed white noise will inform you for certain. 

You don't need a subwoofer you need two.

I have a pair, the input level and crossover are set so I don't notice them.  However, if one sub is offline I immediately appreciate the sound as flat or less dimensional.  I don't know why but to me the greatest benefit of the subs is the effect on the upper registers, smoothing and airing them out/ opening them up.

I use a REL wireless set up, it really helps with placement not having to be tethered with speaker wire, but it does need AC to power and the SMPS on the transmitter needs to be replaced with a LPS.

How do I know if I need a sub woofer?

When you don"t have one.....or two.....

I guess if I get a sub or two my quest for a very good sound system will be over...thank god. 

I have owned many speakers over the years. There were a few that did not benefit from subs, but they were also cheap, off the shelf, great for dorm parties, speakers.

With quality speakers I believe most benefit. My full range Acoustat 1+1 speakers are really wonderful on their own with jazz, solo, and small ensemble performances. However, with orchestral, pop, or rock they are just OK. Add a pair of subs (originally Vandersteen, but now Rythmik) and the details explode. It seems to me that hard to drive speakers really open up with subs and become more musical when the bass duties are removed. I use an SPL Crossover (active) to limit the signal to the mains.

I have heard some amazing full range speakers that do not have subs. Surprisingly, many of the owners of these great speakers frequently add subs and are amazed at how much better they are. Subs need to be properly dialed in to make a difference (in my opinion both low and high pass crossovers provide the best benefits). 

Ultimately though, the end user has the final say. We are really here just to enjoy the music... I hope.