No dilly-dallying, no fence sitting. Yes or no. See, I believe that Ichigo will appear to have killed Grimmjow but that like most Kubo characters, Grimmy will pop right back up (in the next chapter or in 25 more). Therefore I have to vote "no." I believe, personally that no character who has made a Bleach Beat single can die, but Grimmjow's death at the moment seems so essential to the plot and to Ichigo's Hollow development.
Will Ichigo kill Grimmjow?
Not necessarily about Bleach, but 2 links to some (pedantic?) posts about shipping:
A Lucky Guess
3 Stages of Shipping