A reference from John to Genesis based on the Tanakh?
It is curious to consider whether there may be an intended link here. In the LXX the term 'μονογενὴς' only appears in a handful of Psalms, and once in Judges:
Then Jephthah came to his home at Mizpah. And behold, his daughter came out to meet him with tambourines and with dances. She was his μονογενὴς; besides her he had neither son nor daughter. (Judges 11:24, ESV / LXX)
So going with the general assumption that the LXX was widely known/referenced in Jesus' day, I'd rule out that the recipients (Nicodemus, or the recipients of John's Gospel) would commonly take the term μονογενὴς as an explicit call-back to Abraham and Isaac based on the Tanakh alone. The term is so otherwise rare that there's no clear link inferred purely by Jesus' use of this phrase in his discourse with Nicodemus.
A reference from Hebrews to John based on the New Testament?
Assuming an understanding of John to have been written/circulated earlier, I'd say it's more likely that there was an intended reference here. With Jesus having used the term earlier it would then be more likely the author of Hebrews who could have intended a linked usage, or observed a clear parallel with Abraham and Isaac.
If Hebrews 11:17 was the only verse to go on here, I'd perhaps be asking whether there was an intended link to Jesus at all, as the author of Hebrews does not commonly draw parallels to Jesus in the text. However, verse 19 follows the verse rather explicitly:
Abraham reasoned that God could even raise the dead, and so in a manner of speaking he did receive Isaac back from death. (Hebrews 11:19)
At face value, in the telling of Abraham and Isaac - where nobody actually died, it seems almost a touch strained to suggest that Abraham's faith was in God resurrecting Isaac rather than saving or replacing him. The author seems to be invoking the raising of the dead as an explicit reference to Jesus, in which case it should not surprise us that they should also use μονογενὴς to reference Jesus' own phraseology about himself. A link here seems possible.
I'd suggest that this Question orders the passages incorrectly, asking whether Jesus was intending to use the term in light of a parallel with Abraham. More likely, the author of Hebrews was drawing the parallel between the cases, and may have drawn on the phraseology used by Jesus in his conversation with Nicodemus.
This passage is part of a sequence of patriarchal stories, in which the author does not tend to draw explicit parallels with Jesus, despite the significant number of contemporary parallels many interpreters have since recorded. The author does not seem to prioritise the drawing of such parallels, but here in v17-19 between the usage of μονογενὴς and the resurrection reference, there seems to be sufficient cause to suggest there was an intended parallel.