Download speeds can increase dramatically. There’s no theoretical limit — it’s all up to what the remote server can provide. But, if all the files you want to download already download almost instantaneously, you don’t necessarily need more speed.
However, for streaming, you only require a certain amount of speed. For Netflix HD streaming, Netflix says it will take 5.0 Mbps (Megabits per second). Other services — from YouTube to HBO Go — should require a similar amount of bandwidth for their HD, 1080p streams. if you’re using Netflix’s 4K UHD stream — and you’re probably not — that will require 25 Mbps. Music streams will require much less bandwidth than video streams.
Take this into account. If you’re using a Netflix HD stream, upgrading from 25 Mbps to 50 Mbps won’t help you. But upgrading from 5 Mbps to 15 Mbps would definitely give you some wiggle room, allowing you to handle multiple streams or a stream and some downloads without problems.