Keyboard and mouse? No.
360 Controller? Manageable but some shots can feel hard to make with a controller. I don't even want to imagine dog fighting the more advance fighters later in the game without a joystick.

>>2948421
>Would I need to buy a joystick to play them?
Do you want to feel like you're filling in a spreadsheet or dogfighting in outer space?

>>2948421
I am 99.9 percent sure that a joystick is a requirement, and that there is not option to keyboard/mouse the game. That being said you could use a 360 controller but it will handle like shit.
Invest the 30 bucks to get a Logitech wingman extreme from your local big box or Amazon. That way you can also enjoy classics like wing commander and a ton of other great space/flight sims.