"Random" encounters? No. Scripted encounters occuring at camp, sure. I agree with Eugerome, more specifically
Said this in other threads and I'll say it again: random encounters are a waste of players time.
If they are truly random here are a few issues:
* The encounter can wipe the party if it is low, and the party will steamroll them if they are full on resources. So this actually encourages to rest more often and with more resources.
* They are unlikely to add any story elements.
Sure, adjusting the randomness could be a thing - for example as a DM I don't throw a random encounter at a party that is low on resources. But then again, I do refrain from throwing random encounters anyway as they don't really further the plot of my campaigns.
Any encounter occuring at your camp should be related to the story or more specifically, the characters. For example, vampire hunters coming for Astarion after you let him drain a townsperson, someone who's heard of Wyll as the 'Blade of Frontiers' showing up as a fan, or rival, another Shar worshipper with a mission somehow connected to Shadowhearts arriving and requesting assistance, or someone she's acted against and 'forgotten'.
Having a singular 'encounter' as you locate a new campsite in the next acts, or even in this one (where exactly... IS camp?), and story encounters to defend them after either heinous actions, or attracting attention of local baddies, would be fine. Even in Dragon Age: Origins, the best 'random encounters' (which are debatably random) are the ones with direct story tie ins, or that introduce important story hooks, for example, Wynne and the 'Vessel of the Spirit', or Zevran.
I don't personally find much value in 'random' encounters, loot is already plentiful enough they are not needed for that purpose, there are enough combat encounters, and I don't think they would help to fix the rest issue. I believe people who rest often would just rest even sooner to avoid being low when they DO get a random encounter. I prefer not to rest much anyways, typically only using short rests once all of my short rest abilities in my party are used, using consumables sparingly, and rarely using long rest spells. Typically I can get to level 4 without long resting at all, but it is definitely easier to do so with a rest, and may be necessary if the Harpy fight goes wrong.