Good question. The Prescriptive Residential Wood Deck Construction Guide,  recognized by all the major codes, does allow ledgers to be attached to an engineered lumber rim joist with I-joists as long as the rim (band) joist is at least 1 inch thick and made from OSB or “structural composite lumber” such as LVL. This is usually the case in modern homes, but some older homes with I-joists used thinner material. Table 5 in the Guide shows the ledger fastener spacing for solid wood and engineered rim joists. The spacing is reduced for 1-1/8-inch engineered lumber and reduced further from 1-inch engineered lumber.

For BVLZ connectors, however, Simpson Strong Tie states very clearly that the ledger must be 1½-inch sawn lumber or 1 ½- inch-thick engineered lumber “with equivalent specific gravity”.  Specific gravity a measure of density (compared to water). So items with the same specific gravity will weigh the same for the same volume. Most engineered lumber rim boards have equal or greater density than sawn lumber, so you would probably be OK if the rim board were 1½-inch thick. But thinner  rim-joist material like you have is not allowed by Simpson’s specs for the BVLZ.

Short answer, probably NOT allowed, but you can always contact Simpson’s technical services department, to see if they have a workaround.

Read more about Band Joist Connections.