Can carboxylic acids like act as nucleophiles in substitution reactions?
Carboxylic acids can act as nucleophiles of course. Consider reactions with isobutene or thionyl chloride (although base certainly helps in this latter case). However, whether it's in $\mathrm{S_N2}$ or $\mathrm{S_N1}$ reaction mechanisms is another matter. If you beast something with enough heat it will usually react. I would not be surprised if a carboxylic acid reacted with triflouromethanesulfonic anhydride without base. It's still $\mathrm{S_N2}$ as mechanistic studies have shown the S=O bonds do not open up like acyl electrophiles.
I suspect you would need to resort to a continuous as opposed to a batch approach to push a reaction between the acid and an alkyl halide without using any base. Expose the reaction to high temperature (I'm thinking 250C and higher)  for 5 seconds or less under continuous liquid flow.