We have dug out the bulbs on several plants and found that some tiny
bulbs are growing from the original bulb. Question is will these tiny
bulbs produce a new gladiola if separated and planted? Seems logical
that they would.

Indeed, they will. Like any bulb, the flower produced next year is directly
proportional to the size of the bulb, this year. The tiny bulbs won't produce
flowers next year. However, if you treat them like onions -- try to fatten up
the bulb by giving the plants full sun, rich soil, good drainage, and lots of
fertilizer -- they will probably bloom the following year.

This method of patient increase yielded over 40 blooming gladiolus plants, from
a single original bulb, in my Wilmington, DE garden, over a period of about 5
years.

Wendy
Sequim, WA (Zone 8)