I add cubes durring mlf all the time.
Bubbles are not really an effective method of monitoring mlf anyway , it's possible to have mlf complete with hardly any detectable bubbles anyway .
Only testing such as paper chromatography can give you a real indication of mlf progress .
I put my cubes in the carboy , rack the wine off the gross lees into the cube carboy , add optimalo , pitch MLB and put the airlock on .
After 4 weeks I test for mlf status using paper chromatography . The cubes may have sank by this time.
So it's up to you , there is no technical obstical to oaking durring mlf . The oak won't impede progress.
I'd recommend using cubes or larger format oaks post primary and durring ageing
Chips and oak dust are not intended for post primary fermentation oaking , they are intended to add tannin and mask green flavours durring primary when there is active live yeast to metabolize and buffer the harsh fast release the small format high surface area of oak dusts and chips.