Periodically, I check my Start-up menu through "Run" just to make sure nothing has been added that does not need to be there--Quick Time & Adobe is the worst about doing this. Anyway, I have a Data Start-up web site that I use to check out Start-Up files/Names, and Apple Push is not in that data base. I did a search with Google for that term, and this is what I found:

Monitor and manage your iCloud storage through Vista and Windows 7 with this free applet.

If you’ve updated your iPhone, iPod or iPad to iOS 5, you’ll no doubt be aware of the existence of iCloud, Apple’s online storage service. If this is the case, iCloud Control Panel for Windows is what you need to stay in control of your storage account.

The utility, as the name suggest, does install as a Control Panel applet, but it can also be accessed through the notification area of the taskbar in Vista and Windows 7. With a couple of clicks, the app enables you to monitor the amount of storage space you have available – the 5GB provided free of charge may seem like quite a lot to start with, but once you start to synchronize photos and files, it’s surprising how quickly this can be eaten.
Now I don't have an IPod or any other device similar, but I do have ITunes that I installed not too long ago. Not sure if this is part of ITunes or not. But then again, recently Amazon gave me a free music file (song) for buying a music CD through them and I think this might have something to do with Apple Push because I had to download something else to get the song. Like I said, not sure where I got this Apple Push and not sure if I need it or not. Don't like to un-check something if I don't know what it is and what it is for. Thanks in advance for any info you can give me about this Start-up file.