Hi David,
You can certainly do this and it will give you something somewhat reasonable, but it is far from ideal for a couple of reasons:
1. Junction reads will not map
2. There is more information to allocate multi-mapping reads when considering transcript structures and abundances (i.e., exons in the same transcript should have similar counts, ignoring biases).
I would recommend the following approach instead:
1. Run RSEM with a full transcript GTF file and with the --output-genome-bam and --sampling-for-bam options. This will generate a genome-level BAM with each read mapped to a single location.
2. Use bedtools or something similar on the resulting genome-level BAM and a BED file of exon intervals to generate counts for those intervals.
With this approach you use the full power of RSEM.