It should be fine, it will just need a long charge before you use.
I have one I bought off Amazon. I used it a couple weeks ago to jump a dead battery in my junky car (it has a bad alternator that needs to be replaced...just haven't had time to do it yet). It worked fine.
I will say that with the lithium ion jump start, you only get a couple chances to start the car before it dies. Pulling power from the battery into the car rapidly depletes the lithium ion battery. For example, I used it twice on my completely emptied car battery and it went from 100% charge to about 60%.
So if you're having bad issues with the car battery, don't expect to get more than a couple tries before the lithium ion jumpstart battery is depleted.