Can I safely infer that a sadhaka who starts Nama Japa without bhava can be atomically transformed into the next stage?
Irrespective of sect, irrespective of one has faith or not, anyhow having uttered name one surely gets the fruits.
श्रद्धयाsश्रद्धाया वापि यः कश्चित् मानवः स्मरेत्।
दुर्गाम् दुर्गशतोतीर्णह् स याति परमा गतिम्।।
यथेंद्रश्च कुबेरश्च वरुणह् साधको यथा।
अभक्त्यापी च भक्त्या वा यः स्मरेद् रूद्रगेहिनीम्।
सुखम् भक्त्वेह लोके तु स यास्याति शिवालायम्।।
Any human with faith or not, remembers Durga, get liberated from hundreds of miseries and attains the highest goal.
The way Indra, Kuber and Varun are 'Sadhaks', the one devoted to Durga, is also a 'Sadhak' in this world.
The person who with devotion or not, remembers Rudragrihini Durga (the wife of Rudra), gets happiness in this world, and after death attains Shivloka.
Shrimad Bhagwatam, 6th Skanda, 2nd Chapter,
सांकेत्यं पारिहास्यं वा स्तोमं हेलनमेव वा
The great realised souls know this that even in sanketam (addressing for other work & not jaap), while making fun, while taunting, or while showing disregard to someone, a person utters the name of bhagwan, his all sins are burnt.
पतितह् स्खलितो भग्नः संदष्टस्तप्त आहतः।
हरिरित्यवशेनाह पुमान्नार्हति यातनाम्।।
The human that while falling, sliping by legs, his body being crushed or in Snake bite, getting burnt by fire and even while getting injured, chants the name 'Hari Hari', due to compelance, is not tortured by Yama.
Just like anyone without knowing the reality of Amrit drinks it, still the Amrit makes the drinker immortal, just like that uttering the name of the bhagwan even without knowing, is bound to provide the fruits. (Because, the quality of a vastu doesn't follow faith, it is bound to show it's effect even if used unknowingly).
pumān vimucyate sadyaḥ
siṁha-trastair mṛgair iva
If one chants the naam, even in a helpless condition or without desiring to do so, all of one’s sinful reactions immediately depart, just as a lion’s roar causes the small animals in the forest to flee in fear.
This same was once the topic of debate between, Dindayal Goenkaji & Hanuman Poddarji. Dindayal ji believed that without knowing the meaning of the name or having faith in it, the Naam jaap, has no significance. While Poddar ji had the belief that faith or no faith, the name will surely, give liberation.
Thus once while discussing on this topic, Dindayal ji said that, "In English, Ram means a sheep, while to us RAM is sakshat parabrahma. So suppose, while dying an English man thinks of Ram the sheep, and utters it, will he be liberated?"
Replying to this Hanuman Ji said, "yes man will definitely be liberated".
Goenka ji asked for an explanation.
Hanuman Ji said, even without faith or knowing the meaning of the word if one utters the name of the bhagwan he will definitely be liberated. This is something just like knowingly or unknowingly if a person cuts an onion he is bound to have tears, by eating poison is surely to die. Just like that, the name too uttered gives liberation. As naam and naami (the bhagwan) are no different. " Then he reminds Goenkaji about the story of Ajamil from Bhagwat Purana.
Shrimad Bhagwat Puran, 6th Skanda, 1st chapter,
That foolish man was living his life this way, and by then his time of death has approached. Now he started only thinking about his son Narayana. Then Ajamil saw that three servants of the Yama have approached to take his soul. The had a noose in hand, they had crooked face, and the hairs on the body were erect. Upon seeing the servants of the Yama, Ajamil got anxious an utter the name 'Narayana' in a loud voice. Seeing this, the servants of Vishnu ran to protect the soul of Ajamil from Yamadootas, as they thought, Ajamil was remembering lord on his deathbed.
6th Skanda, 2nd chapter-
Ajamila due to the company of maid servant, had ruined his Dharma, he was fallen because of his evil deeds. Because of violating the rules he was being about to put into the hell, but just by remembering the bhagwan's name once he became liberated.
Thus, it is evident that naam jaap knowingly or unknowingly is bound to give liberation.
Do scriptures provide more information about bhava promotion?
Shrimad Bhagwatam, 6th Skanda, 2nd Chapter says,
The sinner like Ajamil, on his deathbed under the pretext of his son's name, what are the name of the Bhagwan. Even he got Vaikhuntha, so what to talk about those people who remember the name of the bhagwan with faith and devotion.
... Because by remembering the name of the Lord, the mind of the person get completely engrossed in Guna, Leela and form of the Bhagwan, & the mind of Bhagwan itself consider that person as his own.
Puranas mostly don't talk on Bhaav in open lines, thus the Bhaav upasana of any sampradaya can only be learnt by Guru.