No if you use the tools correctly then you'll be a major advantage because it's a lot easier to use the Facebook / Twitter API than to construct those things yourself. If you're building a telco probably not a good idea to use someone else's telco infrastructure, if you're selling chairs, it's probably a good idea to buy phone service, rather than construct your own infrastructure.
Does iCloud work on Android? Does it work on a PC? I doubt dropbox and instagram are in any danger because they have barriers to entry that Apple is likely unwilling to take. How many dropbox subscribers are going to go away? Probably not many. Could they lose a bunch of free users? Certainly.
I don't have the data, but I wouldn't be surprised if DropBox had a disproportionately large market of users that were purely on the Apple stack -- and tended to share with other Apple users (when they did share across ppl).