If that will make you feel better then yes, it can count as an approach. However if you want to break through your shell and anxiety I'd recommend you to stop counting approaches and try to have a friendly small talk like that anywhere you go.
Ideally, and I mean IDEALLY so don't beat yourself up now, the social part of your life should feel like a "one big blur" to you in a way that you can't really point out how many conversations you started and nor you can distinguish whether this thing you did was legit approach or not.
Some will tell you that a real approach is only when you go after a girl from the get go, others will tell you something different. Who cares. Just focus on what you do and worry about overall direction of your actions, ignore pointless details and you're good.
Ideally, and I mean IDEALLY so don't beat yourself up now, the social part of your life should feel like a "one big blur" to you in a way that you can't really point out how many conversations you started and nor you can distinguish whether this thing you did was legit approach or not.
Some will tell you that a real approach is only when you go after a girl from the get go, others will tell you something different. Who cares. Just focus on what you do and worry about overall direction of your actions, ignore pointless details and you're good.