Traditional Anglican ping, continued in memory of its founder Arlin Adams. Of course Anglicanism could survive without bishops -- it always has.
I don't know about Anglicans - but the main function of the bishop in the Catholic Church, aside from his connection with the Apostles, which is documented on every bishop's ecclesiastical record (that is, "consecrated by X, who was consecrated by Y, who was..etc.") - is his teaching function. There have been times when Catholic dioceses have gone for a long time without a bishop, and it has never been good. When Spain was under Muslim domination, there were many sees without a bishop or where the bishop had been appointed but could not occupy his chair. The resulting corruption or loss of orthodox teaching had a terrible effect on the Church in Spain and actually was one of the things that made the Inquisition seem like such a good idea.
It was initially an investigation, limited to baptized Christians only and focusing particularly on the clergy, into the state of Catholic belief and practice, which was not very healthy after so many years of neglect. One of the reasons it became so politicized and went well beyond its mandate was the lack of local bishops strong enough to resist power-crazed local "Inquisitors" and stand up to the secular political forces that saw the Inquisition as the ideal way to get back at their enemies.
Other places that have had no bishops have had difficulties - the Church never really grew in Japan, for example, and the delicate situation of bishops in China makes the life of the Church precarious.
So, yes, bishops do matter (although the situation may be different in the Anglican Church).