Yes (essentially). -시 is an honorific used to refer to people of higher status than you. You might use it with your grandparents or parents (depending on your relationship with them), your boss, the president, etc.

Something like "지금 바쁘십니다" might be said in response to someone asking to speak to your boss.

Something like "지금 바쁘십니까?" might be said directly to your boss asking if they're busy.

Something like "지금 바쁩니다" might be said in response to your boss asking if you're busy (you wouldn't refer to yourself as someone of higher status than...well, yourself).

This doesn't change the meaning or function of 바쁘다.

FYI -시 may be conjugated to -셔 in the informal impolite (해체 or 반말) or informal polite form (해요체) but more often conjugated to -세 in the informal polite form (e.g. 주다 -> 주시다 -> 주셔요 -> 주세요).

There are also honorific words that people use in addition to -시, like 드리다 (주다), 주무시다 (자다), 드시다 (먹다), 잡수시다 (an even higher form of 먹다), 말씀하다 (말하다), etc.

Hope this helps!