Yes you should be able to observe signals from different sacharide moieties. 1H NMR spectroscopy might be enough do differentiate between homo- and heteropolysacharide. Here is an example paper with the usage of NMR for sacharide structure determination:
In my understanding on this biochemistry, especially in similar compound we can not differentiate from the source i.e. similar or from different origin.
I would suggest to have a look at the resources on the Widmalm group page. They have done extensive work on NMR characterisation including the establishement of a database and a web-based application to aid in structure assignment.
A homo saccharide with the same linkage between all units will mostly display what looks like one set of signals. There will be additional signals for the endgroups as they are slightly different. i.e. there might be alpha and beta anomers present.
A heterosaccharide will most likely display a much more complicataed spectrum with different sets of signals for the different sugars. Looking at the anomeric region is a good indicator as Vyacheslav points out.
The complexity of the spectrum will be determined by the composition of the heterosaccharide.