Based on my experience with processors of similar grunt you could do convolution with a 50ms IR if efficiently coded.
Obviously on the cheap end of the spectrum you can get some degree of room correction with a well-chosen set of moderate-order IIR filters and delays + speaker placement. It all depends how perfect you want the result.
As for guitar effects, I have been able to chain the following simultaneously with about 56% CPU loading (this wasn't a practical combination, but just to see if I could handle all my guitar FX at once):
Kokkinizita Rev1 Reverb (this is >25% CPU loading on its own)
Dynamic range compressor
8-band graphic EQ
As @AndyCap pointed out it would depend what kind of overdrive algorithm you want.
An overdrive that sounds ok uses a low-order polynomial (like 3rd order) a few first-order IIR filters, which is all a drop in the bucket for BBB CPU. It's probably lower CPU than the dynamic range compressor.
If you really want to do serious modeling to the degree where you can't discern the difference between the software overdrive and a real tube pre or stompbox then you will probably use as much CPU as the BBB has just to do that one effect.
On the other hand, all I listed except the reverb are not very large adders.
Back in the day I used a Digitech RP20 Valve, which accomplished everything on far less substantial CPU power than the BBB. As for overdrive, these were real analog circuits, sent out a DAC and received on an ADC. I actually really liked that multi-FX unit. I wished Digitech had stayed on the track of analog and digital hybrid hardware rather than jumping on the DSP modeling bandwagon. Now 25 years later the DSP modeling is getting good enough to look at again.
On the other hand, I have a lot more fun messing with Bela. My plan is to eventually use Bela to take the Digitech RP20 concept where I wished it had gone: I'm planning to chain channel 1 into an analog FX chain, then post-processing in channel 2 and out...
I seem to recall the latency chugging all my FX in series is <4ms when channel 1 is chained into channel 2 (so 2x the nominal latency).
Channel 2 uses time-delay effects like echo and reverb, so the added latency when that channel is active is not such a big deal.