Would he be surprised of the fact? Did he suspect something? After all, he was extraordinary intelligent and other than that, he had his spy Severus Snape amongst the Death Eater's Inner Circle.
We don't know
I couldn't find anything in canon that would suggest the Dumbledore knew. That doesn't mean he didn't, however.
But based on what we know of Dumbledore and Voldemort, we can gain some insight.
We learn from Cursed Child that Voldemort had Delphini with Bellatrix after the prophecy was given (I don't have the quote right now, will check when I get home). Now from what we know of Voldemort, he does not love; and everything he does is for his own ends to increase his power or improve his security from death. Assuming that he knew of the prophecy, having a child with one of his servants in order to put said prophecy into motion was no act of love or romance. I would suggest, that if Dumbledore knew about the prophecy as Voldemort may have, he would not at all be surprised by Voldemort's actions. After all, it fits Voldemort perfectly to use others for his own ends.
Remember also, that Dumbledore died almost a full year before the Battle of Hogwarts. We don't totally know when Delphini was born, but it's suggested that it was soon before the Battle of Hogwarts. It therefore could very well be that Voldemort did not begin this endeavor until after Dumbledore had died. Obviously, Dumbledore would not have the ability to learn about this if he was already dead.
Finally, Snape was indeed privy to many of the Death Eater's secrets, but not all of them. Voldemort told nobody of his Horcruxes. He would certainly keep the information about his daughter among as few people as possible.
Ultimately, my conclusion is that Dumbledore likely did not know. However, we can't be totally sure of that.
Did Dumbledore know?
There's simply no evidence to show that he knew about Voldemort's indiscretion with Bellatrix, not is there any specific indication that Snape was aware either.
Would he have been surprised?
I suspect not. He was well aware that Hogwarts had spawned a megalomaniacal monster and he clearly had a very low opinion of Mr Riddle. Given Voldemort's proclivity for surrounding himself with compliant henchpersons, it probably wouldn't shock Dumbledore to find that Voldemort had dallied.