Do I need the sampling frequency in order to gain periods out of FFT? Currently I am using the transformInPlace() method from here.

for a project at university. 
First of all I thought FFT would be the perfect solution for my problem, but
now I am not so sure anymore. 
I have to alter a certain component of a software called LIMBO.
LIMBO is a load intensity modeling tool.
Every webpage has a trace that records the number of site views during a fixed period of time.
This leads to trace files like this data.

You can see lots of (time, arrivalRate(time)) pairs. This is all LIMBO gets as input.
The goal is to search for dominant periods within the noisy trace via the FFT.
The problem are the time values of the (time, arrivalRate(time)) pairs.
For a fixed time (for example 1 day) the page counts views. The total number of views than is
stored inside arrivalRate(time).
Then the page listens for another day in order to calculate the next arrivalRate(). This process is repeated
the whole time.
So, the time values inside the trace (for example 0.5,1.5,2.5) are not necessarily days (They  could be seconds, weeks or even months as well). They are abstract and depend on individual fixed listen period of every webpage mentioned above. (probably listen period  is called sampling frequency but I am not sure) 
Therefore the information about the listen period of the page can not be retrieved out of the trace file.

My question is:
  Is it a problem to know nothing about the listen period of the given page if I want to calculate and interpret dominant periods
after a FFT has been applied on the trace file?

For example I use this formula to calculate $f_i $(the frequency of the $i$-th array position)

$i$: current position in the array

$N$: length of the array

$f_s$: the sampling frequency that is probably not revealed in the trace (so far I just used values like "1" or the median of all arrival rates in the trace)

$i = N f_i/f_s$   (so I use $1/f_i = {\rm period}_i = N/(f_s i)$ for calculating the $i$-th period)
This is DSP – everything that defines time or frequency is only measurable with respect to your sample period; so without that, your FFT output is but a relative measurement.

In short: If you can live with giving information like "events per sample period", then you're fine, if you need to say something about "per hour" or so, well, that information has to come from somewhere, and if you're not feeding in that information into your system, it can't have it.