Most definitely.  I found that during my sleep I need a higher basal
rate than when I am awake.  Regardless of the time I am sleeping.
However, I also found that I needed to have different basal rates at
different times of day when I was awake.  That did not match the rates
when I was sleeping. You see because of my job when I am required to
work over time, not very frequently thankfully, I can end up working 8
- 10 or 13 hour shifts anywhere in a 24 hour period.  We don't have 3
separate 8 hour shifts per day, which would make things a lot easier.
If I sleep during the day or I sleep during the night or
mid-afternoon, my BG will rise unless I set a slightly higher basal
rate than when I am awake.  This is why when I was injecting insulin
via a syringe and attempting to use lantus only for a basal insulin it
did not work correctly.  I had to add humulin N(NPH) at bedtime, timed
to peak at a specific time during my sleep and wear off by an hour or
so after I wake.

So when I injected via syringe and used Lantus, I used 3 separate
insulins, 2 to cover my basal needs and 1 to cover meals and make
adjustments.

With the pump I use 1 insulin and simply program various basal rates
at the appropriate times and of course program meal boluses to cover
what I eat.