C41 has no couplers in the soup, so the film will be blank after the bleach except for minor staining from coupler traces bled from previous colour film runs.
But as long as you use the developer only, you would get some image - not particularily good, but not worse than the average large scale lab would deliver. Indeed, one large lab I knew did their b/w film batches in their regular E6 primary developer (which is quite straightforward b/w developer), with a dedicated b/w stop and thio fix afterwards.
It won't damage the C41 process either - if any, only strongly wrong color stock (which doesn't occur in suitable volumes today) would. The only thing labs are scared of is back-coated movie stock, and that not because it damages the chemistry, but because the back coating (used for anti-halation and as a discardable surface which protects the film base against scratches) will come off as bits and pieces of goo all over the processor if that is not set up with a special backing stripper for movie stock.
Sevo