If they could credibly threaten your infrastructure then it makes sense. If they have no real organized hacking capabilities then no. But the US has already attacked Iran through computers before with Stuxnet and is the world leader in software and networking knowledge so it does make perfect sense for Iran to disconnect its networks from outside.

You might also have to consider the propaganda campaigns the US could run against an Iranian population with web access. If the population isn't more discontent now than it already was, "secretly" replacing commercial ad placements on western websites with US propaganda when the requests come from Iranian sources could make them discontent or inflame them further, which is bad for the Iranian government.