You can, but. IR is gonna last you 6 gcds if you use it immediately when the GCD starts spinning. Used after ID, those 6 are Dis+CT+4th+Ph+TT+VT(+gsk, if you pop gsk before LS). If you use it a GCD later, IR is missing Disembowel and picking up Life Surge>Full Thrust, which doesn't get a benefit from the 10% crit buff. You can just delay BotD in the gcd by ~1s same as with B4B to get the same benefit without missing an IR-buffed GCD.

Shifting IR+BotD a gcd later is nice when using potions in fights such as A3S, where you don't get the full 60s of your initial BotD to run down, so you *need* that extra buffer to get 3 gsk in phase 1, but this is a discussion of the optimal no-potion opener.