Does recoil accumulate from this?
Yes, but progressive recoil will be reset in the Action Phase where you just spend a Simple Action firing.
(in your case it will go up to 11 recoil of which 10 is compensated and 1 uncompensated which mean you get a negative dice pool modifier of 1 dice - in every second action phase, i'll break it down for you at the bottom of the post).
If you're thwooping a grenade in between full auto bursts, then you're never resetting your progressive recoil.
True, which mean he will gain some progressive recoil which will result in one point of uncompensated recoil in every second action phase.
But firing in Single Shot mode is typically resolved as a simple action. Since he is using his other Simple Action in that Action Phase for something else than shooting (Take Aim, for example) this will reset progressive recoil when he starts to shoot again.
IP 1: Ready Weapon + Take Aim.
IP 2: FA 10 round burst. Positive dice pool modifier of 1 dice (and/or accuracy) from the previous Take Aim action. 10 point of recoil and 10 recoil compensation = zero RC left, but also zero uncompensated recoil.
IP 3: SS grenade + Take Aim. 1 extra point of recoil but with no remaining recoil compensation this mean you get 1 point of uncompensated recoil = negative dice pool of 1 dice. RC is is reset to 10 RC during the Take Aim action.
IP 4: FA 10 round burst. Positive dice pool modifier of 1 dice (and/or Accuracy) from previous Take Aim. Zero RC left but also zero uncompensated recoil.
IP 5: SS grenade, take aim. 1 point of uncompensated recoil
IP 6: FA 10 round burst... Zero uncompensated recoil...
or
IP 1: Ready Weapon + Take Aim.
IP 2: FA 10 round burst. Positive dice pool modifier of 1 dice (and/or accuracy) from the previous Take Aim action. 10 point of recoil and 10 recoil compensation = zero RC left but also zero uncompensated recoil.
IP 3: Take Aim + SS grenade. RC is is reset to 10 RC during the Take Aim action. It also provide a positive dice pool modifier of 1 dice (and/or accuracy). 1 point of recoil reduce RC from 10 to 9, zero uncompensated recoil.
IP 4: FA 10 round burst. 10 extra points of recoil but with only 9 RC this means you get 1 point of uncompensated recoil = negative dice pool modifier of 1 dice.
IP 5: Take Aim + SS Grenade. RC is is reset to 10 RC during the Take Aim action. It also provide a positive dice pool modifier of 1 dice (and/or accuracy). Zero uncompensated recoil, 9 RC remaining.
IP 6: FA 10 round burst... 1 point of uncompensated recoil...
(having said that; progressive recoil rules in SR5 are a bit over complicated if you ask me - it get a lot easier to resolve in the next edition, but anyway - this is how you would resolve it in this edition).
