The phrase "arguably impossible" is correct and usable in written English.
It can be used when discussing a situation or task that is open to debate regarding its feasibility or likelihood of success.
Example: "Completing the project in just one week is arguably impossible given the scope of work involved."
Alternatives: "debatably unfeasible" or "potentially unattainable".
This is a herculean, and arguably impossible, task.
Moreover, human physiology is so complex, and medical science's understanding of its bounds so limited, that drawing a line between an exceptional but clean performance and a drug-enhanced performance is a tricky, arguably impossible, proposition.
Binding the first movement's setting of the medieval hymn Veni, Creator Spiritus and the second movement's setting of the final scene from Goethe's Faust into a single organic structure over the music's 80-minute span is the essential, and arguably impossible, challenge of this work.
Judgements which are really difficult, arguably impossible sometimes, about the right thing to do regarding a child and their family.
While it's arguably impossible to pinpoint the greenest school in the land, we can pinpoint which colleges and universities are ahead of the pack.
The desire to create a fair, just reality for both people establishes the conflict and is arguably impossible to satisfy with an ethic that focuses purely on individuals and not on relational communities.
In particular, the oscillator function is difficult to understand in terms of gene-gene interactions, and would arguably be impossible to rationally design using current methodologies.
The design of a high-quality genotyping array with millions of SNPs for GWA in the grapevine is, arguably, an impossible task because of the difficulties associated with assaying diversity across such a diverse genus.
A similar effect is arguably inherently impossible for those sequences that are already highly efficient in their unmodified form, as is the case for the bcl-2 targeted siRNA 1+ 2. No silencing effect was detected when the conjugates were applied without lipoplexes.
Arguably, it's impossible to reach with existing technologies.
Arguably, it is impossible for any individual to exemplify all the possible ways of being human or all of the possible ways of being rational.
