Absolutely.
When I picked up a uke of my own, my goals were simple:
1. Enjoy myself
2. Become comfortable enough to strum basic songs without error
3. Discover whether this was something I wanted to continue and grow with.
Every one of these is an emphatic yes. The very first time I held an 'ukulele and strummed it I thought it was great. When I picked it up again (after a 7 year hiatus) I remembered that feeling and it has only increased. At first, I was barely capable of holding the damn thing, much less making any tolerable sounds. I was convinced I had no musical talent, but after a couple of weeks I was actually strumming chords that <gasp> sounded like chords! By the end of the second month, I was blasting out basic three-chord songs and was delighted.
And the best part is the more I improved and the more I played, the more I wanted to play and the more I wanted to learn. Now, songs I thought were completely out of my reach because of some tricky chord switches and fretboard dexterity (like "Build Me Up, Buttercup") are falling into place with minimal agony, and I've started to work on things like fingerpicking and some rapid fretting.
But the very best part is that it keeps getting more and more enjoyable every day.
As one of our leaders once prematurely ejaculated: "Mission Accomplished!"