I've never tried it, but the key would be adjusting the Digital Speed and Digital Center settings in the analog input section of MAME's in-game menu.
When you substitute a button or joystick direction for an analog control in MAME, it doesn't simply go full left or full right.
Digital Speed adjusts how fast the virtual analog control is moved from rest to limit and Digital Center adjusts how fast the virtual analog control returns to center after you release the button or move the joystick to center.
So with reasonable settings, the car would turn farther left the longer you hold the joystick left and you can bump the joystick between center and left at a certain rate to keep the car pointed where you want. Of course you're only going to find the proper setting through trial and error and it's still not going to be as good as having real controls.
If you just want some racing games on your cab and aren't hung up on specific games, just install the ones from this spreadsheet marked "joystick" or "any"
https://docs.google.com/spreadsheets/d/1pJLy8JgRF7dL1X3CcDyDLKOLSIJs4gYZY4DLI0pmnmE/edit#gid=0On a side note Midway Arcade Treasures 3 (PC game) doesn't support analog input for great games like Hydro Thunder.
The analog controls were ditched and the games are set up to be played with a keyboard making them play better on a standard cab.
The games each have individual .exe and can be launched via command line. -f for fullscreen.
(EDIT: Just for clarification, the games added for MAT3 Deluxe do not support analog controls. MAT3 Deluxe includes games from MAT1&2 which do support analog controls)