Yes, absolutely. It's called "style shift." There's a whole book about it, and it's covered in brief in A Dictionary of Advanced Japanese Grammar, but in short:
The most common place to hear style shifts is when the background style is polite. In most conversations in です・ます style between native speakers you will hear shifts to plain form. Here are some reasons it happens:
- The speaker is expressing their feelings emphatically. (So, to go back to your question: -しい adjectives often appear in plain form even during a polite conversation. e.g., I'm eating lunch with a superior and take a bite of something delicious; I'm likely to say 「おいしい！」, not 「おいしいです」.)
- The topic has shifted from, say, business to "So, what are you doing this weekend?"
- The speaker is switching from an explanatory to conversational tone.
This is far from unique to Japanese; you hear it in English conversations as well; it's just that we don't tend to mark politeness level syntactically. (And yes, there are also shifts from plain to polite style.)
Shifting style in a natural way takes a long time to learn as a JSL speaker. You know how you get to the point where you don't have to think about は and が anymore, when you can just feel which one is right? Style shifting is like that but takes even longer. It's probably not even something you can study, per se; you just have to listen to and participate in lots and lots of conversations with native speakers.
Oh, one interesting thing: if you ask Japanese speakers about style shift, they will often deny that it happens and/or not notice that they're doing it.
(Hat tip to Prof. Amy Ohta at University of Washington, who has studied this topic at length and taught me most of what I know about it.)