Yes, but at a slower rate. Each of your spells hits your opponent for 3+ while Eidolon is pinging you for 2. You win when your opponent is at 0 life, it doesn't matter if you're at 1 or 20.
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I prefer a mix of Inspiring Vantage and Clifftop Retreat (2 of each). Inspiring Vantage is strictly better in your opening hand. Arid Mesa is also good in this deck because it helps your Searing Blazes hit the landfall trigger.I run Vexing Devil in my mono red burn, and it does well because my opponent often takes 4. Typically you don't win with burn by swinging creatures. You win with damage spells. Goblin Guide and Swiftspear are great turn 1 because you'll likely get 3-4 damage out of each, but they aren't generally how you close out a game.
1) Most modern decks run spells that trigger Eidolon. Eidolon can easily do between 4-6 damage while also providing a body that threatens to swing or block. It's very efficient at only 2 mana.2) Fetch Lands help thin your deck (providing a very slight improvement to your odds of drawing the spells you need) and in burn decks specifically they can make it easier to hit your landfall trigger for Searing Blaze.
@heterokingis: This is a pretty standard burn shell, the win con is to hit the opponent with high-efficiency spells.@SuperMegaPanda: I would personally drop 2 Searing Blaze and 2 Shard Volley for 4 Lava Spikes. Overall I think it looks good!
Some more ramp would be fun! Maybe 2-3 Nykthos, Shrine to Nyx, and 4 Utopia Sprawl. 2 Heroic Intervention could help protect the board.