Yes, Nickelodeon would still be popular without its iconic green slime for the simple fact it is entertainment for children and some adults. Over 90% of its programming is animated entertainment and also consists of some great classics like, " I Love Lucy" and " The Brady Bunch". Nickelodeon has always provided content appropriate for all audiences and enjoyable entertainment.
Nickelodeon, in my opinion, would not be the same without the iconic green slime. Unless Nickelodeon plans on replacing this icon with something as catchy or memorable, then I would suggest keeping it. As a company, it's all about the fanbase and about logo/company recognition. The green slime is an important part of this.
The iconic green slime associated with Nickelodeon is not what made the network popular. There is just a strong association between the two. The network would still be hugely popular for a wide variety of other reasons, even without the green slime. Actually, Nickelodeon's use of green slime made it more popular.
Children growing up from the mid-80's up until 2016 can tell you one of the most iconic things about Nickelodeon is the slime. It is something children dream about happening to them and has been the wish of child fans throughout the years of watching the show. Without this slime, Nickelodeon wouldn't have had a factor that set it apart and may have slid into the background such as their competitor Cartoon Network.