It isn't theoretically impossible at least, in light of the recent post on hexamine reduction - Post 378615 (https://www.thevespiary.org/talk/index.php?topic=9162.msg37861500#msg37861500)
(Organikum: "hexamine to methylamine a old new way?", Methods Discourse) - but I doubt that it would be possible to add the hexamine and ketone at the same time to an Al/Hg mixture - but you may be able to do it as a one-pot reaction, as in first adding hexamine and Al/Hg, followed by the ketone and more Al/Hg when the reaction is over.
However, for best yields and purity, first make your methylamine and purify it, then use it for reductive amination.
I know that you are probably familiar with.....
(https://www.thevespiary.org/rhodium/Rhodium/hive/hiveboard/picproxie_docs/000379029-file_jnuc.gif)
Dissolve 140g (1 mole) of hexamethylenetetramine (urotropine, hexamine) and 157.5g (1.05 moles) sodium iodide (or 174g (1.05 moles) potassium iodide) in 1000ml of hot 95% ethyl alcohol (190 proof grain alcohol). 243g of bromosafrole (1 mole) is then added and the solution is allowed to stand until no precipitation occurs. A stream of HCl gas is then run into the mixture where the precipitate is hydrolyzed, dissolves and ammonium chloride precipitates. The ammonium chloride is filtered off and the alcohol of the filtrate is removed through distillation under reduced pressure. Purify the crude amine left by releasing the free base with NaOH solution (45g NaOH in 135 ml water). Extract the oil with ether (or toluene, methylene chloride etc.) and reconvert to the HCl salt with a stream of HCl gas. Filter the crystals formed from the ether.
To substitute iodosafrole use 290 grams (1 mole) or chlorosafrole 199g (1 mole). When substituting iodosafrole omit the sodium iodide (or potassium iodide).
https://www.thevespiary.org/rhodium/Rhodium/chemistry/tcboe/chapter7.html (https://www.thevespiary.org/rhodium/Rhodium/chemistry/tcboe/chapter7.html)
This is that reaction that you can leave be and go on vacation.
Pr(+)tium
According to https://www.thevespiary.org/rhodium/Rhodium/pdf/hexamethylenetetramine.pdf (https://www.thevespiary.org/rhodium/Rhodium/pdf/hexamethylenetetramine.pdf)
secondary halides are unreactive towards hexamine. I'd really like to hear from a credible source that this reaction actually works...