No they were not. Yes there were runs on local supermarkets - not directly after the wall came down but instead a few days later when they introduced the "welcome money" (Begrüßungsgeld) so even ordinary people had some money to spend on stuff. But bananas were still available, except maybe in the most frequented locations, for example the Ulrich supermarket at Bahnhof Zoo station (the same place the GDR elite used to shop for their supply of cognac, champagne and related stuff).

People confuse those days with the events about a year earlier when Poland eased the restrictions on their people to travel to the West. Since Berlin was the closest destination countless Poles chose that as their first stop - and that actually did lead to supermarkets being sold out on many goods, among them bananas, but more importantly critical supplies like toiletries. That was when some of them actually introduced quotas on customers, so they wouldn't run out for the locals. This lasted for quite a few months, so when eventually the East Germans started to show up those shops actually had a lot of experience to handle the surge in demand.

That's gonna very hard to prove. I tried to find info on this but failed to produce a source that is able to say something definite about this topic. There are however plenty and plenty of reports of people living in West-Berlin at that time and I looked a bit around and asked my uncle (who was living in Kreuzberg in 1989) : it's all heresay so nothing water proof but : There were runs on many goods in West-Berlin that were not available or very restricted in the GDR : This includes Bananas and other exotic fruit, Jeans, Vinyl LPs, coffee, sex shop goods, western cigarettes, wine, beer (!), liquor and even luxury stuff like Champagne. A lot of people from the GDR were confident that everything the people in the West had was better and (there were not wrong for most goods) and plenty of them spend their 100 DM welcome money on stuff they wanted to lay their hands on for a long time. Mind you, 100 DM was a lot of money in that time, but that didn't stop people from spending it on worldly pleasures they had envied their western brothers and sisters for a long time.

So to come back to your question : It is likely there was a shortage of Bananas and similar goods in Berlin in the first few days after the Wall fell, but you can expect the demand was quickly met after a few days. If Bananas were completely sold out in all of West Berlin I can not say, but tbh I somewhat doubt it. The stories with the run on Bananas is cute and funny but I guess it's place in history is a bit exaggerated (maybe due to a famous cover of the satire magazine Titanic showing a girl with a peeled cucumber saying 'Zone Gabi with her first banana')