"I have a feeling she probably had a pretty good time as a groupie," Gilpin tells PEOPLE of Eileen, who squares off against Craig Robinson's music teacher in the School of Rock-esque NBC sitcom.
For starters, Gilpin reveals that viewers will quickly learn during Wednesday's premiere episode that her character "was the inspiration for the [Dexys Midnight Runners] song 'Come On Eileen.' "
Though Gilpin, 54, didn't dish all the dirt on Eileen's "major backstory," she ultimately thinks "all that experience is fantastic for what she's doing. I don't think anyone can get one over on her. ... She can use her experience to help people have fun but stay engaged and stay on the right path."
Though, adds Gilpin, "[Eileen's] life was pretty crazy for a while."
RELATED VIDEO: Craig Robinson Breaks Down His New Show Mr. Robinson with an Epic Freestyle Rap
The blasts from the past aren't just limited to what's happening on screen, though – Gilpin just happens to be sharing a sound stage with her former Frasier costar Kelsey Grammer's daughter Spencer, whose character Ashleigh Willows has her own wild side: "[She] plays a teacher who moonlights as an exotic dancer," teases Gilpin.
"She has a very saucy part," Gilpin adds. "And I love how she's playing it, too, because she's very seasoned. She's a chip off the old block."
The two actresses even had a full-circle moment when filming began: "I took my 11-year-old twins into the makeup trailer and introduced them, and I realized I met Spencer when she was their age," says Gilpin. "I just love that we're working together. I can't believe it. She had to drag me across the stage in one of the first scenes that we did together, and I was like, 'Do you know how many times your dad dragged me across the stage?' It's just amazing."
Mr. Robinson premieres Wednesday at 9 p.m. ET on NBC.