As with any gene, ability to get good -/+ populations will depend heavily on transcript expression and depth. Do you have a way to confirm the +% matches what's expected? For example, we have a GFP reporter that works really well. +% matches exactly what we see by flow. However, they are 100% blasticidin resistant and we can hardly detect the resistance gene (BSD).

If you can't confirm fraction of +% cells, then it can still work if you only really care about positive cells, and it is okay if negative cells are inconclusive.

Theoretically yes, you can add any sequence to the reference. But often in single-cell you get dropouts, so 0 when the gene is actually expressed, and some genes are not well sequencable- or mappable in single-cell (or RNA-seq in general). The dropout problem is especially tricky for classification, because you might mislabel many cells as negative, despite it's just a technical 0.

You need a pilot before investing big money fully relying on a single gene. Maybe the transgene harbors a fluorophor, so you could do flow sorting before and then load +/- cells on different 10x reactions, or at least tag cells by hashtags.

Is it known whether the transgene has transcriptional consequences, so you could track +/- cells by expression profile of relevant genes, or in high-dimensional space by UMAP/PCA/etc for relevant downstream genes?

Bottom-line: Without pilot experiments I would never rely on a single gene in scRNA-seq.