Yes you can - yosuke and lab have nothing to do with relationship or number of days that have passed, there's just a specific list of things to do I order to unlock the lab:
Do yosuke's quest
- attend Friday party
- meet Yosuke at night day after party
- get the thing for him from science student (random event during the day)
- attend 2nd party
- meet up with yosuke again to give him the thing, he will ask for pizza
- cook pizza in the kitchen
- meet up with yosuke, he will point you to kan's room
- attend party to break into Kan's room to get lab key
- run until you reach lab