According to the HTSeq-count documentation, you can specify on what type of feature, you want to assess the counting:
-t feature-type, --type= feature-type
feature type (3rd column in GFF file) to be used, all features of other type are ignored (default, suitable for RNA-Seq analysis using an Ensembl GTF file: exon)
Thus if you use "-t gene", you should get all reads within a gene-locus (frankly, I haven't tested it).
Denote, that overlapping features will appear in this scenario more often and more reads will be "ambiguous" .