Yep, that'll work just fine. Use 5-6 layers of newsprint, and overlap it well. Keep a hose handy to water it down and prevent it from blowing away as you work, and do it in sections, adding mulch as you go. The grass will decompose fairly quickly in the summer heat; it you mulch it now, it should be ready for fall planting.
Cheers, Sue snipped-for-privacy@earthlink.net Zone 6, Southcentral PA