How do you know if you need to add a sub (without auditioning one, I mean)?

There are very few systems that do not benefit from subwoofers and bass management. However, adding cheap subs without a dedicated 2 way crossover is frequently worse than having no subs. To add subs correctly you either need a room control system with bass management or a calibrated mic measurement system like Dayton's Omnimic along with EQ capability. Trying to do it by ear is very difficult if not impossible. 
Doing the DIY thing is a good way to get higher quality subs at a better price and there are some very capable plate amps available. I personally prefer passive subs with outboard amps and crossovers. I would never go less than two 12" subs or four 10" subs. Contrary to lay instinct, larger drivers are not "slower" than small drivers and they have significantly less distortion. Get the largest ones you have room for. 

So what does anyone think of the idea of using a Loki as a very inexpensive experiment to see if more bass even suits me.

If you have a standing wave in the room, EQ and room correction won't do anything to fix it!

Forget the Loki and at least try a pair of subs...subs do so much more than only deep bass for a system...then decide exactly what configuration works best for you...

How do you know if you need to add a sub (without auditioning one, I mean)?

short answer is you don't

So what does anyone think of the idea of using a Loki as a very inexpensive experiment to see if more bass even suits me.

The Loki may be a solution but it may also cause you problems. I am making an assumption here, and you may already know this, but the Loki is more than likely a 4 band peaking style e.q. with a very low “Q” so depending on where the center point of each band is you may be boosting or cutting the wrong frequencies for your room. For an example in my room boosting the frequencies between 40 and 50 Hz (approximately 1/3 of an octave) gives me a very full and large sounding kick drum, but if I boost 63 Hz just a little bit (the next 1/3 octave above 50 Hz) than that same kick drum becomes very boomy. My guess is that each channel in the Loki covers a much larger range than 1/3 of an octave. I don’t know what the range is but it wouldn’t surprise me if each channel covered a couple of octaves or more.

Another option that may be worth looking into would be a miniDSP unit. It should be comparable in price to the Loki but I believe it has several bands of parametric e.q. capabilities where you can select the center point of the frequency that you want along with the “Q” so you can better tailor the unit to the needs of your room.