Resequencing your sample is not going to make it any less heterozygous. I am assuming that you are working with a diploid organism? Please update your question and specify the genome size and ploidy of your organism (the type of organism will help us update our answers, too).
The answer, yes, you can use Pilon + short reads to correct the PacBio assembly even with a highly heterozygous sample. To do so you should use the
--diploid option in Pilon to let it know that there will be heterozygous sites. The way that it corrects heterozygous SNPs and heterozygous indels is different, and it seems to perform best with SNPs and sometimes does not correctly identify heterozygous indels (source).
Pilon itself doesn't handle phasing, but just corrects with whatever reads are in the
bam file that it is provided with. The end result of providing a
bam with reads from both haplotypes is that the corrected sequence will be a mosaic of the dominant allele at the heterozygous site as was observed in the short read data. This may or may not select for some alleles based on sequencing coverage bias of Illumina sequencers.