no
there’s no such thing, really, as a “desk that’s non-dealing”
the expression “non-dealing desk broker” just means a broker that doesn’t use a dealing desk
“without the intervention of a dealing desk” is correct - it just means, as explained above, that trades are (allegedly) passed on to a liquidity provider without being individually inspected by a broker-employed “dealer” which would cause delays
note, though, that there’s no reliable way of telling whether a broker is “NDD” just because they claim to be - people who have worked in the industry will tell you that not everything is necessarily as it appears to be, and that these terms like “NDD” and “STP” (straight-through processing) and “ECN” (electronic communications network) don’t necessarily mean anything much at all; this illustrates why it’s so important only to use brokers who are regulated by a proper regulator (which means, in effect, regulated by ASIC or FCA or CFTC)