CNVs are listed as SVs (structural variants) in VCF files. I believe an VT=SV is anything that is over 50bp while indels (VT=INDEL) are for sizes under this. As to your question of copy number--I think sequencing technologies typically catch deletions and so most deletion SVs will appear in a VCF file while those that are duplications would not likely be well-measured with sequencing technologies. I am relatively new to the VCF format, though, since I work mostly with array data. You can pull data for your region from 1000 genomes and check what SVs are in the region with the following code:
tabix -fh ftp://ftp.1000genomes.ebi.ac.uk/vol1/ftp/release/20110521/ALL.chr4.phase1_integrated_calls.20101123.snps_indels_svs.genotypes.vcf.gz 4:152890286-153092741 > genotypes.vcf
cat genotypes.vcf | grep SV
This will pull out all of the SVs in the 1092 1000G samples.
What you're asking though is how to display differences with this reference sequence. I'm not sure the VCF file is the best way to do this. Some kind of read depth analysis might be more helpful and give you a semi-quantitative measure of copy number. People doing more sequencing may have better insight.