You'd be hard pressed to find a better fit for our needs than Burns. You'd have an equally hard time finding a better situation for a player like Burns in FA than the Oilers.
The problem is, all of the things we can offer Burns as a free agent (dollars, term, role, competitiveness), he can also get from the Sharks. And the Sharks have the added benefit of being his home for the past 6 years and also being in California.
If he did decide to move on, I'd have to think our chances of getting him would be good (how about that...3 years in a row where arguably the top UFA on the market chooses us).
Cap wouldn't be a problem either. With Burns coming on board, Russel would be less likely to return, meaning $3.1M of Burns' salary would be covered. You'd also have to think that either via buyout, trade, or expansion claim (in descending order of likeliness), Fayne would be gone as well. That's $6.725M of cap space cleared up to give directly to Burns. That would make him the team's highest paid player and comparable to the deal Seabrook got, and only about $1M less than Byfuglien's.
I'm guessing Pouliot is the guy we lose to expansion. Between him and Hendricks, we've got $5.8M to give new contracts to Draisaitl, Lander, Pitlick, and Kassian (or their replacements). That's also not including the existing cap room we already have.
Of course, it still leaves us looking for an extra $5M or so to re-up McDavid the following year. Does the cap go up $5M over the next 2 years? Worry about that 2 years from now, I say.