Yes, it looks like it can "currently" be done, because Trail Ridge Road through Rocky Mountain National Park is currently open. (At this time of year, any cold front could close it for the season).
Take I-70 east about 40 miles from Beaver Creek to the Silverthorne exit 209. Take CO highway 9 north to Kremmling (wonderful photo ops all along the east of the Gore Range mountains), then US 40 east (about 40 miles) to just before Grandby, CO. Left on US 34 through RMNP ($20 entrance fee, if you do not have an annual National Park Pass) and over Trail Ridge Road (lots of elk photo ops, but get there before Wednesday as there is a storm predicted that might close it for some time) to Estes Park (a nice place to stay overnight -- better than Boulder, if you have the time).
From Estes Park, you have two choices to Boulder, CO -- Colorado 7, the Peak-to-Peak highway (most scenic and spectacular at this time of year) or US-36 (fastest, but kind of boring). If you stay in Estes Park instead of Boulder, the drive to DIA can be relatively short and direct using US-36 to I-25 to E-470 Toll Road.
Can it be done? Definitely yes, and it is worth it. Too much driving time? That is up to you. In my opinion, this drive along the east of the Gore Range, through the Byers Canyon of the Colorado River, then over the Continental Divide through RMNP should not be missed. Versus the relatively bland drive from Beaver Creek to DIA on I-70? -- it is a no-brainer.
Start out early from Beaver Creek, as you will have 5-6 hours of driving plus (many) stops along the way for scenic photos, versus about 3 hours direct from Beaver Creek to DIA (really, no scenic photos on that particular route).