yes you can. but the imac late 2013 27" is the first model of the imacs which is capable of 4k at 60Hz, lower dates (mid 2013 or early 2013 or even lower) cant support 4k at 60Hz.
but it strongly depends on your OS and 4k Display type.
with the latest OS 10.11 or 10.12, 4k/60Hz over Displayport or MiniDisplayPort is supported.
lower systems like 10.8 or 10.9 dont support 4k at 60Hz.
"With OS X Yosemite v10.10.3 and later, most single-stream 4K (3840x2160) displays are supported at 60Hz operation on the following Mac computers:"
- imac 27" late 2013
that could mean that if you buy a multistream 4k display, you could only get 30Hz, which could result in mouse lag or other lags.
so whats left, is to find out, if your desired display is a SingleStream or MultiStream Type.
i hope i summed it up correctly. if not, please correct me.
thanks