Yes, it is plausible and even probable that Jesus taught within the synagogue at Magdala.
Sorry just one more thought came. In Jesus time, they gathered in homes for their weekly sabbaths. Within the homes of Men/Woman who offered their homes, Jesus even stating I coming to your home forget his name, which is written in the Bible. Jesus preached on the weekly Sabbath, Woman’s homes who were wealthy, well known within the Community, who offered their homes to Jesus in teaching, preaching. Synagogues also were used as schools for teaching the Word also, children etc, future priest etc.
Sabbaths for the Jewish Families today are they not also still observed within their homes? The Temple, was when all would gather from other Nations commanded by God to come before Him, coming from surrounding areas on their Yearly Feast Days. Historically written also the Romans considers when they did? why?
So Mary Magdalene coming from a wealthy Noble family,( prostitute? really?) her brother Lazarus, her other sisters Marys, had more siblings also? Not surprising, they would open up their Homes for Jesus preaching, teaching, on their weekly Sabbaths or stay with also, was it? They gathered as a family and most families not like today all lived together, in Jesus times did they worship on their Sabbaths within their homes also?
Historically written, within their Hebrew Israelite traditions, Torah Laws, could not wonder far from their homes on their weekly Sabbaths either.
Mary M could not go to the Tomb, until the Sabbath was ended, nor could she go to the market to purchase oils, spices for Jesus burial. She did so the day before the Sabbath, was against their Religious laws to go far from their Homes on their Sabbaths, to shop, work etc ?
One also finds St Paul preaching long into the night, beginning of the Sabbath within a home of who?
Forgive me!!

just find the life and history of Mary Magdalene very Interesting.
