I think it is important to have access to the Internet all the time. Although it may not be seriously necessary, it would be good. Then you would be able to reach any information you want or need at that instant. It would save a lot of time and even from trouble. You could use it as a guide while traveling, you could learn about any medical situation you want if there is an emergency, you could talk on the Internet with people, learn things you need and so on. It would come in very handy most of the time.
Although it has a lot of pros, having access to the Internet all the time also has its cons as well. The Internet is capable of killing your precious time. If you like spending time on the Internet a lot, being capable of reaching it all the time, you may get too distracted and it may start occupying more time than the amount of time you usually use to surf on the Internet. It might become more isolated when you can constantly spend time by yourself using the Internet. It can make you less out-going or completely isolated.
In conclusion, it would be useful and practical to be able to connect to the Internet at any time in any place. It can be a great profit but you would have to keep yourself from going with the flow and from losing yourself on the Internet completely. It would depend on you, whether if it is very useful or if it is no good to you and will waste your time.