Yes; likely many.
That's unless all your parents, grandparents, great-grandparents, great-great-grandparents and further back were their parent's only child in which case there are no corresponding cousins of that degree.
An article Cryptic Distant Relatives Are Common in Both Isolated and Cosmopolitan Genetic Samples includes a table reproduced at the ISOGG website under the heading How Many Cousins Do We have? The simplified version here shows that, despite the dramatic reduction in chances of detecting more distant cousins, results typically show more matches to more distant cousins. Simply, there are more of them.
The many more distant cousins connect on the many more lines down from shared ancestral couples, and in times when families were typically larger than today.
Just because cousins are detectable does not mean they'll be a DNA detected. To do so they have to also have taken a DNA test with results in the same database as your's.
Size matters. The chances of detecting a fourth cousin in the larger database are more than four times those in the smaller.
Most genetic genealogists have the experience of having cousins as DNA matches but not being able to find the connecting recent common ancestors. We usually look for surnames in common in both family trees. But our genealogical brick walls mean we know a smaller fraction of surnames in the more distant generations.