I want to convert a coat closet to hold a ventless washer/dryer combo. The back of closet meets a bathroom, so I'm hoping plumbing isn't a problem. This model only needs a standard 120v three prong plug, which I know will have to be installed. The closet is plenty roomy right to left but it's a tight fit back to front . Will this work?

You need to know what you can access through the closet wall without ripping out any expensive bath stuff, and how far away the waste vent is above the washer drain (or are you saying you don't need venting for the water? I don't believe that), and what your local code is for the distance to the vent. You can map all that out yourself. You need to know your house total amps, and if the circuit panel can add the required 30 or 40 amp circuit. The place selling you the w/d will be able to tell you.