In combination with the advanced edit panel this can work pretty well… just deselect all the note categories except delay, copy (continuous)paste.
Someone also made an awesome set of scripts for it called PushBack (forum post with explanation) and PushBackKeys. The latter is only downloadable via git for now though (server issues). It allows to set delay values quickly for the whole track, every edit step. You can even step the cursor to a group track first and it’ll edit the delay values for all tracks in the group. Imho it works way more intuitive than the groove function inside renoise.