No, syncing your jailbroken device won't make it crash. iTunes doesn't recognize whether its a jailbroken device or not. All it does is go to your apps and copy the data associated with them, along with saved preferences and calendar entries, contacts and stuff. Actual system files that make your device jailbroken are not backed up. Also if you decide to sync it make sure you don't update the os when it asks you, or your phone will be un-jailbroken. But other then that everything will work fine.
Oh and iPhone explorer (which is now called iExplorer) is a file browsing program. So if you launched it and plugged in your iPhone, you'd be able to browse your phone as if it were the hard drive on your computer. So if you know the directory at which app data was stored you could copy those files off your device and replace them later. I still recommend PKGBackup because it works the same as above, only its automated so you don't have to do any of the file copying yourself. And if you integrate it with dropbox, you don't have to worry about storing the backup on your computer.