No, not always.
Що may have several functions:
A demonstrating pronoun (cf. English what)
Що ти читав учора? — "What did you read yesterday?"
Since we have free word order, the following sentence is equally valid:
Учора ти що читав? — literally, "yesterday you what read?"
This requires no comma.
A subordinating conjunction that join a dependent clause (cf. English that or which):
[Я думаю], → що → [ти був там]
In Ukrainian, the clauses (both dependent and independent) have to be separated with punctuation (comma). The square brackets in quote above denote the clauses, and the arrow shows dependency.
In other words, The comma is needed to separate the dependent clause, not because of що.
- Я думаю,
що ти був там — here, що is optional, it can be skipped. The comma is retained.
- Я знаю, який твій улюблений колір — "I know (comma) which is your favorite color" — here we have a totally different conjunction, but the pattern is the same: a dependent clause requires comma.
- Він розповів, чому він був там — "He told (comma) why he was there" — yet another conjunction.
The same applies to many Slavonic languages, and this is the reason why you may encounter people who write English and make typically Slavonic mistakes, for example:
I know, (comma) that you've been there;
I like, (comma) when you sing;
Please, (comma) tell me... — although lexically "please" is a particle (unlike an adverb in English), some linguists consider "please" as a separate sentence similar to "be kind", and that's why it requires comma.
Even more, dependent clauses are separated with commas in Romance languages, like German:
Der Mensch ist Etwas, das überwunden werden soll. — Nietzsche.
Man is something (comma) that shall be overcome.
Here again, comma separates the main clause, "man is something", and its dependent one, "shall be overcome".