If you surrender to Him, then you remain subservient to Him.
You don't become Him.
A true monist would never surrender but would seek for the unfathomable impersonal Brahman, after he subdues his senses and vrittis (racing thoughts).
AFAIK, pretty much all hindoos consider God to be all pervasive. Not just the monists but even the dualists (the Hare Krishnas) claims that Krishna/Vishnu is all pervasive. The vishwa roopa/virat purusha/cosmic man encompasses and pervades everything.
And I agree with you that paramatman is dormant where there's no reflecting medium (mind), but paramatma is not missing in such objects.
To the dualists, the word paramatma and parabrahman are used to address Krishna/Vishnu. So yeah, it doesn't matter whether he's impersonal or personal, he's everywhere.
And i don't recognize words like physical energy and consciousness energy. As far as advaita is concerned, there's only one energy, that is consciousness. There are no two energies in advaita.
You'll have to use sanskrit scriptural terms and its English equivalents, if you want to discuss hindoo monism coz the ones you're using, can lead to confusion.
A Jivatman's surrender is a passing phase until it becomes Him (God), the ultimate goal in advaita when one becomes infallible and perfect in ones dharmic actions and lives to ones full genetic potential.
When the jivatman has surrendered the paramatman becomes active with the 'purusha' spirit overruling the 'dehi' spirit in the functioning of the jivatman. Paramatman is not normally present in atman because the 'purusha' spirit is missing.
To understand this, consider the following:
Brahman is the total energy of the universe (physical energy and consciousness energy), whereas atman is only the consciousness energy of the Universe, and is under the direction of its ‘dehi’ spirit. So in my synthesis of advaita atman is not Brahman. It is this dehi spirit that makes electrons move in atoms, other chemical bonds take place and the living being witnesses, lives, thinks and ages.
However, the atman is unable to witness or act until its dehi spirit is activated by Paramatman's ‘purusha’ spirit: and this is subsequently deactivated at death when it again ceases witnessing and acting and lies dormant until it is reactivated by purusha again. Once activated the entity becomes a jivaatman (a living being) which then witnesses and acts in accordance with the soul force of consciousness energy incorporating the three guna blends through the differentiated direction of dehi spirit.
When the jivatman surrenders to God (transcending the gunas), the dehi spirit is overruled by the purusha spirit of the Paramatman and then the jivaatman becomes God whose witnessing, awareness and actions are infallible and perfect in the dharmic actions that it undertakes.
Surrender is no longer an appropriate concept as the jivaatman no longer exists.
Want a hard answer!