Kaladin's journey with depression has been quite explicitly not about finding poor ways to cope, but rather confronting it and reaching acceptance, while also not letting it define him.
He and Syl becoming romantically involved would not sully his story with depression. Sometimes a romantic relationship is helpful, though, and there's no reason to pretend it's not in a fictional story. It becomes an issue if the reason for romance is relief (both in reality and if that's the message in a narrative), but at this point in Kaladin's story it so clearly would not be that. Regardless if it's a relationship with Syl or someone else.
To add, it's okay to do stories about maladaptive coping mechanisms, good even. Specifically in Kaladin's case, though, a relationship with spren or human would not be that because of what he has already gone through.