Oh yes, love is definitely a loaded word, in life and in therapy even moreso. Many types of therapy wouldn't allow for that type of love at all, really, it could be seen to compromise the therapist's objectivity, the client's feeling of security, etc.

I'm in what you might call psychodynamic therapy though, therapy attuned to the relationship w/my therapist, and I perceive it as a particularly warm and caring type of therapeutic relationship, compared to my experience with psychoanalysis and my understanding of other popular forms like CBT.

Not to say there's never love in other types of therapy, but I don't think it's at all typical to express it as such or get that deep.