I just got an email from Madeleine Beekman which supports Randy:

With respect to haploid individuals, it is not possible to have an inbred
individual if you are haploid. Issues may arise when the queen and her
mate carry the same alleles at many loci as then the resulting offspring
becomes homozygous.



I also found a paper by Robin Moritz which supports my notion:

Inbreeding depression in classical quantitative genetics is explained
by an increase in homozygous loci in diploid organisms. The classical model
must fail in haploid or hemizygous individuals because in these cases it is
impossible to increase the degree of homozygosity.

Nevertheless it was possible to find inbreeding effects in haploid
individuals of haplo-diploid populations. Figure 1 shows
the factors affecting inbreeding depression in haploid and diploid individuals.
Figure 2 shows a decrease in MDH and ICDH activity
in drone flight muscle mitochondria depending on the inbreeding coefficient
of the mother queen.

The genome has no influence on the inbreeding depression of haploids.
Nonheritable maternal effects and heritable cytoplasmic structures should be
the only causes of inbreeding depression in the case of haploidy.

INBREEDING EFFECTS IN FLIGHT MUSCLE MITOCHONDRIA OF Apis mellifera L.
Robin F .A. Moritz  Rev. Brasil. Genet. VI, l, 59·70 (1983)

Nevertheless, this was written in 1983. We now may be able to detect changes in the genome which would be symptomatic of inbreeding, and could produce effects like those above, even if the drone has only one copy if this genome.

PLB

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