Therefore, my question is if there's a minimum data rate that enables OFDM?
No, there's other limiting factors.
Like, if the rate is too low, it's probably hard/impossible to split the data unto datastreams with an even lower rate.
No, that's easier the slower you go. It's not more of a problem at low rates.
You're forgetting why we're doing that splitting: A very high-bandwidth signal sees a wide channel – and a wide channel experiences frequency-selective fading, due to multipath propagation. If you have for example a direct path and a path reflected off some structure, then for one frequency, these waves would interfere constructively, for a different frequency, destructively. If you have both frequencies in your wideband signal, then you're in trouble because you can't revert that effect with a simple multiplication.
So, you split your wideband channel into frequency-flat subchannels. Problem solved.
At some point, it doesn't make sense to split any further. If your channel is flat already, splitting it doesn't make it "flatter". On the contrary, you're incurring the problem that channels change over time (that's due to movement of the transmitter, receiver, or obstacles and reflectors, as well as due to oscillator imperfections), and if you increase your signal duration enough, you will hit a wall where your nice flat channel sadly becomes a channel that's not nice at all but changes faster than you can follow.
I'm asking because I'm trying to trigger OFDM with my dev boards which send raw 802.11n packets at 1mb/s, but it's not working.
OK, you don't "trigger" OFDM. OFDM is a method of transporting data. IEEE 802.11n is indeed an OFDM standard. It's multiple MHz wide, in the microwave region: of course you'd use OFDM there. These channels very much are multipath.
So I'm thinking that the rate's too low for OFDM.
Nah. No such thing. There's digital voice transmission schemes that do OFDM at around 700 bits per second. There's probably a few HF (or below!) modems that do even slower OFDM for long-reach comms across half the planet.