I wonder what would happen if a new account leveled only on bots?

[Kaawumba-1133]

It doesn’t matter how you level up. Competitive MMR/SR is completely separate from the other modes.

@Kaawumba-1133

New accounts

If a player has never played competitive, his initial competitive SR is around 2350 (38). For new players, MMR and SR are more volatile (35) and SR has been measured to approximately follow the formula: SR change = -3.85 * game + 99.34 (38) until about game 18. So even though everyone starts around 2350, after 18 matches, there is a wide variation in ratings. To fall to the depths of bronze, or climb the highs of top 500, requires significantly more games, however. That is, newer accounts tend to be artificially close to high gold.

(35) Overwatch Forums
(38) Initial Competitive Skill Rating, Decrypted