Your question "can G-d descend?" is a little like the question "is G-d anthropomorphic?" since the former implies that G-d is a body. For clarity, I will address the question of whether G-d descends, but it will also encompasses some of the latter.
Did G-d have to descend to investigate a matter in Genesis 18:20 and 21?
A literal reading of the Bible thinks so:
“G-d said, ‘the cry of Sodom and Gomorrah is great, and their misdeeds are very grievous. I will go down now and see whether they acted as [indicated in] the cry that has come up to me, then I will destroy them, if not I will know.’”
The phrase, "if not I will know" is obscure. The simple reading has G-d wondering if He heard correctly, to clarify this, G-d will descend and investigate what is really happening. The prior phrase states that if He discovers that the people did not act properly, he will “destroy them.” G-d concludes “if not,” meaning that they were righteous, then “I will know” this and not harm them.
Rashi supports the notion of a corporeal deity descending when he portrays G-d anthropomorphically. Scripture states: “G-d came down to see the city
and the tower that the people built [the Tower of Babel].”
Regarding both stories, the Midrash Tanchuma asks “Does G-d need to descend and see?” it asks. “Isn’t everything known before Him?”
The Midrash explains these stories to be a figure of speech. It informs judges not to make a decision only after a brief insufficient investigation. G-d is all-knowing and all-powerful and does not need to descend to hear or prove anything. Additionally, Onkelos substitutes the anthropomorphic “I will go down” to “I will reveal Myself.” There is nothing that G-d does not already know, He is certainly not taking a trip to learn about circumstances in which He has no prior knowledge. Rather, He is “revealing,” informing them that He is reacting to the evil done. In his commentary to Exodus 19:20, 33:21 and 34:5, Abraham ibn Ezra paraphrases Onkelos and Midrash. In his Guide of the Perplexed 1:10, Maimonides explains the terms “go down” and “go up” is metaphorical, meaning that "going up" indicates that divine revelation is taking place and "go down" means the communication has ended.
Maimonides adds in Guide of the Perplexed 2:45 that all biblical prophecies, with the exception of Moses, were dreams. He writes on 1:10 that G-d's descent is a figure of speech, indicating that the divine decree to render punishment has been acted. Thus, Maimonides says that chapter 18, like the Akedah story, never took place. It was a dream. Abraham dreamed about a conversation with G-d, who descended in anthropomorphic terms. Maimonides will generally recast a biblical story as a prophecy. This greatly angered Nachmanides, who insisted that the stories in the Bible were true events. It could be argued that the Rambam's interpretations greatly diminished the historical significance of the Bible.
 We will not address the part of the story where Abraham attempts to argue with G-d over the destruction of Sodom and Gomorrah. But we will add that the notion that humans can influence G-d to change His mind seems problematic, as it suggests that an all-knowing G-d is not altogether wise and that humans can sometimes have a better understanding of the situation.