When you're serious about engineering a viral loop, you meticulously measure each loop component, and the overall k-factor. A factor greater than one means you are in exponential growth territory.
However, you can see exponential growth with an average k-factor less than one. I've seen it happen several times now, e.g. in my last company and now in two of my portfolio companies.
This phenomenon is due to what I call "viral pockets." These are subgroups of your users that are experiencing exponential growth, i.e. pockets of virality. The overall average k-factor is still less than one, but your service is nevertheless growing at a rapid rate fueled by internal dynamics.
The takeaway is that you should be looking at subgroup statistics to spot these pockets as well as trying to engineer them via subgroup landing pages, emails and other particulars of your viral loop. Once identified, you can focus on optimizing these parts of your user base that you can get to go viral, which by their very nature will start to take over your entire user base.