Yes, Kodi can and can also play gapless MKA files. The only issue is that the time stamps on the CUE sheet are not read correctly. I mean, the first couple of seconds of each song are trimmed if the song selected is not the first (and the album is not played in its entirety from beginning to end). I've noticed this behaviour after ripping Robert Fripp's Exposure and The Beatles' Abbey Road. I'm using an MKA file with a CUE sheet generated using MMH Chapter editor (from the original MKV file). The time stamps on the cue sheet are correct, but are not read correctly by Kodi.
As an example, these are the three tracks of RF's Exposure. According to the time stamps, track 2 should be 2m 24s long, but Kodi reads it as 2m 34s long. Don't know... maybe it has to do with the milliseconds in the cue sheet.
Code:
TRACK 01 AUDIO
TITLE "Preface"
PERFORMER "Robert Fripp"
INDEX 01 00:00:000
TRACK 02 AUDIO
TITLE "You Burn Me Up I’m a Cigarette"
PERFORMER "Robert Fripp"
INDEX 01 01:15:075
TRACK 03 AUDIO
TITLE "Breathless"
PERFORMER "Robert Fripp"
INDEX 01 03:39:802