Yes, it functions without a laptop. A computer is only used for tuning, datalogging, or uploading firmware. I think there are board options that have onboard SD card logging as well. I know MegaSquirt 3 does.
MicroSquirt is a likely option where space is at a premium like minibikes or motorcyles. It's based on the MegaSquirt 2 which is pretty old now (really all the MS designs are), but there's not really anything wrong with or obsolete about it. What I don't like is that it's still expensive and doesn't have an onboard MAP sensor. They instead made the end user have to use a big external one and find a place to put it and the extra wiring.
This is what they haven't been willing to find space for in three different board designs:
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MegaSquirt isn't really the cheap option anymore either. Speeduino has filled that role although I'm digging through the code and even though I'm not a programmer, I'm still having an occasional WTF moment about why they did things a particular way.