Using a undersized anything collet can result in internal damage to the collet. R8 collets typically have three very small “slots” in them that allow for compressing the collet down.
When pressing in say a 3/8ths shank into a 3/8th collet, it should slide in snugly, not tight, snug. When the draw bar pulls the collet in and compresses the collet, the design still has a small gap in the slits but the full compressive force on the shank is achieved. In researching using drills in R8 collets: Universally the answer was NO, this included using Imperialor/Metrics cutters in the opposite type collet. The only reference I could find to a tolerance range was ±.002" and that was a person’s guess. If you were to measure the shanks of cutters I would suspect there is less than a .001" TIR between them.
If when the collet is compressed the slits are touching, then the full compression of the collet isn’t achieved. Torsional forces can allow the drill to slip - galling the inside of the collet.
Cutter shanks come in specific diameters that match industry standard sizes. The actual cutter diameter can be larger or smaller than the shank/collet diameter and is how sizes between collet sizes can be achieved.
Apparently, there are some different collets (not R8) that are commonly used with selected collets. The examples were typically for small machines like out Sherlines but for small bits, 1/32nd or less.
Any drill that IS used in a collet should never have been used in drill chuck (the shank can be damaged) and the shank should match the collet size exactly (use a micrometer to check).
Can drills be used in collets: Yes, but plan of having damaged inaccurate collets that will have more run-out when using cutters because of internal damage not visible.
I think it much wiser to buy a drill chuck that uses a key or wrench to tighten rather than just a keyless chuck.