I accidentally unplugged my hard drive in the middle of a file transfer and somehow corrupted my MFT file, I tried using ntsfsfix and testdisk to repair the boot sector or the MFT file but both were unsuccessful, now my only hope is recovering the files.
My question then would be: Is recuva able to recovery the files even if the MFT is unaccessible?
Unfortunately, no. Recuva requires a working partition in order to act as a 'framework' in order to recover files, so it cannot read 'RAW' (i.e. no working partition) drives.
You could possibly format the drive with a working partition (say, an NTFS) one, run Recuva, go to its settings and turn on 'Scan for non-deleted files' as described here: https://support.piriform.com/hc/en-us/articles/360048410512, then attempt recovery. However, keep in mind that doing so runs a very significant risk of at least some of the data being destroyed in the process, so this would be very much an option of last resort.