Connect new MacBook Air to VGA monitor

Hello,

Not entirely sure if this is the MacBook Air model your wife has but if so, yes it should work.

https://support.apple.com/kb/SP813?viewlocale=en_US&locale=en_US

"Video Support 

Simultaneously supports full native resolution on the built-in display at millions of colors and: 

• One external 6K display with 6016-by-3384 resolution at 60Hz at millions of colors, or
• One external 5K display with 5120-by-2880 resolution at 60Hz at millions of colors, or
• Up to two external 4K displays with 4096-by-2304 resolution at 60Hz at millions of colors

Thunderbolt 3 digital video output 

• Native DisplayPort output over USB‑C
• VGA, HDMI, and Thunderbolt 2 output using adapters (sold separately)"

I hope this helps.