Yes, if you calculate your resistors to be able to handle 1A of current then they can handle anything under 1A.
Keep in mind that if you pick the power rating of your resistors to match exactly the power you are dissipating, then the resistors will get HOT! Pick a slightly higher power rating for the resistors than the minimum required.
(1A)^2 * 0.25Ω = 0.25W = total power dissipation by the current sense resistor
since you have 4 resistors in parallel, each one takes 1/4 of the current, so you actually have
(0.25A)^2 * 1Ω = 0.0625W per resistor (multiply by 4 and you have your original power dissipation of 0.25W)
So you could even get away with 1/8W resistors and they would still be at double the required power rating. (1/8 = 0.125 = 2 x 0.0625)