I presume it's just a small 12V air pump that comes with many cars that don't have a spare tire? No different than a pump you'd get with an aftermarket repair kit? If so you should be able to use it for a slow leak.

But actually I didn't know it came with a repair kit as I've got runflat tires so didn't think to look for it. I do know I don't have a collapsible basket tho' as my audio system takes up that space. ;-)

 

Can I use this as a replacement for my Tirefit which is now 2 years out of date? It seems like it might work or be the same stuff.

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Yes, all these tire repair sealants (aka 'goop') are pretty much the same. They work fairly well but as Wayne cites make a mess of the tire and some can't be repaired thereafter as a result, or at the least require a thorough internal cleaning. They can also wreak havoc with stem-internal tire pressure sensors, if so equipped.
But if you have standard (non-runflat) tires and no space for a spare then sealant and a pump is all that's left. Well, that and a AAA membership [my now preferred method].