Personally, if all of my family is streaming music, video etc... I will randomly get kicked/or lag spikes (but mainly kicked) from the game. As long as you think it won't happen very often, get it. Even if the connection turns out to be horrible, there are other things to do.
Single Player Campaign (known in-game as "Octo Valley")
First off, it has a very fun (but very short) single player campaign. The single player campaign will also provide you with Splatoon's story, but you have to collect "scrolls" to find it out (I haven't collected them all yet
).
Amiibo Challenges
If you want to save up some extra money (like I did), you can get all three of the Splatoon Amiibo to add some extra challenges to the levels you already played in single player campaign (like having to beat the level in a specific time). These are very fun as they add extra challenge and keep you coming back for more. Plus you get rewarded in game money and gear. Both that are (for me) worthless without online. Because the gear that you buy in the shops will only show up in the Plaza and online, and that is no fun if you can't show off what awesome gear you have to the rest of the world.
Local Multiplayer (known in-game as "Battle Dojo")
Lastly there is a local 1 vs. 1 multiplayer mode that has you trying to pop the most balloons (no other game modes). It is fun in short bursts to kill time with your friends but defiantly not as fun as online.
In short, if you have a friend who has this game, ask to borrow it to see how your online multiplayer internet connection is. Because as fun as offline play is, the heart of the game lies in the multiplayer. That doesn't mean that you won't be disappointed if you do get the game, you'll just be missing out.
Edit:
Forgot to mention that there Mini Games you can unlock from the Amiibo Challenges. They are available offline in the Plaza, however they are really meant to kill time while you wait for a online match to start. So basically, they are meant to be played short bursts.