On the connection day it should sync as fast as it can, with no interleaving at first. In terms of sync speed the only effect of G.INP is to restore any speed loss caused by interleaving.
Logically you are right. G.INP (retransmission) applied to a line that doesn't already have some form of DLM shouldn't cause any change in speed.
Likewise, a line running at the full package speed shouldn't see a change in the "attainable" figures either.
But sometimes, reality doesn't follow logic.
On my line, running at full package speed without DLM intervention, the application of G.INP downstream bumped up the attainable speed considerably. Application of G.INP upstream also bumped up the attainable speed - although this disappeared again when upstream G.INP was taken away.
I also recall seeing cases where people experienced real speed increases, even though DLM hadn't intervened before. But I can't even begin to point you at any links...
BTW reported that the majority of lines had seen a small, 1-2Mbps, increase in headline rate - but made no reference to whether this was the effect of removal of DLM. I suspect not, as removal of DLM would normally have a much bigger impact on speed.
You'd imagine this means something else changed somewhere, but less noticeable than "just" FEC and interleaving. Some kind of low-level line coding (such as the trellis coding) perhaps, or the way framing is implemented down at the physical level, but I haven't been able to figure what.