Different probesets are certainly capable of mapping to the same gene on the standard Affymetrix GeneChip platform. Groups of probes are combined into probesets and multiple probesets MAY exist for a gene
And interestingly a resource I have only just found called ADAPT which "describes the many-to-many relationships between Affymetrix™ probesets transcripts and genes, by directly mapping every probe against publicly available mRNAs/cDNA sequences from RefSeq and Ensembl."
As previously stated in some of the excellent answers above it is not just possible, but common.
We have our own system for 'validating' the mappings between affy probesets and transcripts.
Align all of the probes to the genome sequence
Count the number of transcripts that each probe-set is associated with and how many probes hit for each.
Exclude probe-sets that map to more than one gene with a significant number of their probes (promiscuous).
Quality score the probe-sets against actual transcribed sequence (some probes do not actually hit exonic or UTR sequences) and exclude those that fall below a threshold.
Recently I have worked most with the Affymetrix Drosophila 2.0 chip-set and we find about 5% of probe-sets to be unreliable. Most fail because they are promiscuous i.e. one probe-set maps to more than one gene/transcript.