This is advisable to have your post paid connections in Ladakh. Prepaid connections may not work in Ladakh. Air Tel / BSNL are common network at the moment. JIO has been announced in Leh and may work in other region as well.
Your internet connection will work in Leh for sure and your hotels may have possibility for WI FI connection. Though some time internet connection may not work due to remote location and other techical aspects.