Phenomenology explores individuals' 'lived experience'; therefore, I think that observation could indeed be used as part of a mainly phenomenological study (strictly, this would make the study mixed-methods) to for instance, investigate whether respondents actually do what they say that they do; this could help illuminate their lived experience via the researcher enquiring about say, any discrepancies between words and action.
I don't think that observation is the right choice, as in observation the researcher's presuppositions can influence the results. Conducting interview by being open to multiple meanings that can emerge from data would be more suited. Phenomenology emphasizes to explore and foreground the meanings as understood and explained by those experiencing the phenomena.
We can some times see designs as phenomenological and Hermeneutic approach. If we include observation to the data collection are we then toking about likewise approach ?