No. But clearing exploration nodes increases the rewards from the secret room, increasing the chances of better cards (because more cards are given)
Do not think clearing explore areas effects this. I am all lvl 8 and 9, cleared to the third section of heartcoil deeps and still get almost exclusively common out of secret rooms. Once out of every 10 or so I pull a rare. 
Secret room rewards seem to have been turned down, especially the ones on explore mode. They used to be quite rewarding, but now mostly common, and maybe a couple of rare cards.
He is correct though that the further you are in explore mode, the more gold and cards you get, so a slightly better chance of better cards.
In the 4 months I’ve been playing I think I’ve gotten an epic about 2 times from a hidden room. So yeah, very unusual to get anything more than commons.
It’s almost all common gear and gold for me. But right when I was about to gripe about this on the forums, I hit these 2 secret rooms one after the other.
!
!
Never anything close to these two rewards since then. But Calliope and Farideh sure were happy about these two.
Wow. I’ve never gotten a legendary in secret rooms, did t know if that one was possible