##Yup, you always get your ability score bonus.
Despite common misconceptions, D&D5E doesn't actually have "skill checks". It has [ability checks][1], that sometimes get a proficiency bonus, too.

> For example, a Dexterity check might reflect a character's attempt to pull off an acrobatic stunt, to palm an object, or to stay hidden. Each of these aspects of Dexterity has an associated skill: Acrobatics, Sleight of Hand, and Stealth, respectively. So a character who has proficiency in the Stealth skill is particularly good at Dexterity checks related to sneaking and hiding.

Note that it is not a "Stealth check", it's a "Dexterity check" with some extra stuff. Other bits of nomenclature bear it out the same way: characters do not make a "Perception check" to spot something, they make a "Wisdom (Perception) check".

##Proficiency Required
Note that some checks *may* require proficiency. Most common this is seen with picking locks - it's still a Dexterity check, but you need proficiency with Thieves' Tools and get to add your proficiency bonus.

The same thing can happen with skills like Arcana. If the bit of trivia is something that any character living in a magical world might know, the DM could call for an Intelligence (Arcana) check - the DC will probably be low, so characters without Arcana proficiency *could* pass, while smart people with Arcana training almost certainly will. If the DM determines it's something more exotic or esoteric, they can either raise the DC (something every first-year wizard's apprentice *should* know) or *require* proficiency (something only people who've properly studied the subject have *any* chance of knowing).


  [1]: https://www.dndbeyond.com/compendium/rules/basic-rules/using-ability-scores#AbilityChecks