Do all multiple sequence alignments employ global alignment algorithms?
It is dangerous to generalize, as different multiple sequence alignment (MSA) programs may well employ different algorithms. However as the objective is to align many sequences along their whole length, and all MSA programs of which I am aware present the results as such, it is difficult to envisage anything other than global alignment being employed.

For the widely used Clustal W and X, this is certainly the case. Clustal employs a progressive alignment algorithm which involves the heuristic assumption that the most closely aligned sequences by pairwise alignment are a valid basis for the order in which progressive multiple alignment is performed. The initial pairwise alignments (which are used to produce a guide tree) use dynamic global alignment, as does each progressive alignment step, although this alignment is to a profile of previously aligned sequences, and uses context-dependent scoring. 

There is an extensive Wikipedia article on MSA and one of the original Clustal papers is freely available on-line. The excellent book by Durbin et al., Biological Sequence Analysis, contains a chapter on the topic.