If you want it to ride more like a truck, I suppose why not...
I would guess this answer is about being flippant.
Sprint and midget cars get around quite nicely with a solid front axle and apparently they handle also. Like any other front suspension the setup will produce the final ride qualities you are looking for.
Honestly my thoughts building my car ran towards the solid axle.
What I hoped to accomplish was to beat the modern ricer technology with the old stuff but due to lack of backbone and a desire to punish myself in the design stage I caved and designed a independent.
Short answer, it can work quite well.
There is no answer. If someone's okay with a stiff ride, they'll be just fine with a straight front axle. OTOH, someone expecting a Lexus LS460-quality ride won't be happy with any Locost no matter what suspension it has.
About sprint and midget cars - they ride on smooth tracks, not bumpy streets, so it's not a big deal. Also, they're classed such that everyone's on the same suspension, so there isn't even an option to be different.
About comparing the ride of a 1930's hot rod and a Locost, I'd guess that the hot rod would have a smoother ride simply because its sprung-to-unsprung weight ratio is more favorable. As was said, they're very different cars intended for different things, but if ride quality is what it's all about, independant suspension is where it's at. The OP might consider researching why cars went to independant suspension at the front in the first place. Better yet, try and get a ride in a lightweight straight axle car and see if it's tolerable. If it is, you're all set.