I once loaned an old Ibanez mandolin to a guitar player who needed one to play in a pit band for a musical. He returned it with guitar strings tuned to DGBE, an octave above a guitar. (He also included three sets of regular mandolin strings and apologised for not putting a set on.)
The talented session guitarist, one of the most, if not THE most recorded session guitarists in the world, Tommy Tedesco, tuned all of his instruments, guitar, banjo, mandolin, bouzouki, balalaika. . . like a guitar.
I think that the steel strings and closer spacing would make a mandolin very different from a uke, even if you tuned them the same. A mandolin is braced for steel strings and nylon strings would probably not be able to drive the top properly.
A mandolin has about the same scale length as a concert uke. Here are a Joe Zier tenor ukulele, an Eastman MD605 A5 style mandolin and a Harmony "Roy Smeck" soprano uke to compare the size/scale length.
Here's a photo that my friend, Kim took of my Johnson concert reso uke and my Washburn mandolin. The scale length is about the same.