Yes, they will
Though people can still notice if they pass their checks.
For Cunning Caster, you must make a Bluff check with a -4 penalty (for the verbal component), opposed by a Perception check of all who see you. If they fail the check, the spell effect still goes off, but they can't tell it was you casting the spell. If they pass, they will notice that you were responsible for the spell.
For Conceal Spell, you attempt to conceal the manifestation of casting the spell, which means there will be no visual magical effects going on should you succeed. For that, you take a full-round action to cast the spell instead of the normal standard action, but you make no check. Other creatures must make a Perception, Sense Motive or Spellcraft check (whichever is better for them) against DC 15 + your ranks in Bluff or Disguise (whichever is higher) + your Charisma Mod. They gain a bonus on this check equal to the spell level (+2).
If they fail, the only thing they will notice is that you raised your voice to say something, but nothing that makes it obvious that you cast a spell will be noticeable. As the spell has nothing obvious on targets, there isn't much they can do to notice the target was affected by a spell. They still can use Detect Magic and Spellcraft or Knowledge (Arcana) to notice the spell effects, but there won't be anything linking it to your character.
But I would advise against using both
If you want to use both feats, you are effectively using two different feats that will accomplish pretty much the same thing (hide the fact that you just cast a spell). As such, I can see why some GMs might ask you to pick one or the other when casting a spell. I would advise you take only one of those, preferably Conceal Spell, and take Silent Spell instead of Cunning Caster. This way, you can completely conceal the spell manifestation and there won't be any words coming out of your mouth to even suggest you tried something sketchy.
Cunning Caster does nothing to hide the spell's manifestation, which is a real thing even for spells with no components at all, it simply won't be obvious that you were manifesting the spell. Everybody will still notice that a spell was cast, which is concealed by Conceal Spell.