Not at this time. Sequencing is cheap and easy, but hymenopteran genomics is a young field with many more open questions than answers; morphological taxonomy is much more mature, and aided besides by highly specific genital configurations which are, in no small number of cases, the only way currently known reliable of telling two macroscopically indistinguishable species apart. Too, in order to evaluate genomic relatedness precisely enough to update taxonomy, you need your sequence database to be broad as well as deep - unless you already have a broad and deep sequence database of other solitary bees, for example, it's hard to get very precise results out of a given solitary bee's genome. It may not even tell you anything you didn't already know.
In any case, it's not rare in the literature to encounter whole genera categorized almost entirely through analysis of the males' aedagi, with microscopic imagery and line drawings included to highlight features by which distinctions are made. Some of these features are only easily distinguished at SEM scale, so that's what is used.
That said, it's thought among at least some taxonomists that these unique and incompatible genital configurations may be the only thing that prevents interfertility among individuals of these otherwise separate species. So it's going to be really interesting to see what comes out of genomics as applied to the Hymenoptera over the next decade or so - something else that's not rare in the literature is to encounter reclassifications and rearrangements of large branches of the family's taxonomic tree, as phylogenetic research heavily revises prior results. Beyond that, there's a lot else coming out of genomic research into the family, including a rare example of heritable mutualism between a virus and a eukaryote in the form of Bracovirus [1] [2].
So, while yours is a fair question, there is a lot going on with hymenopteran genomics and phylogenetics these days, and my understanding as an interested amateur who does a great deal of reading in the literature is that, for the moment at least, established taxonomical methods still are likely to provide a more precise, albeit still provisional, placement of an otherwise ill-characterized species. In a decade or two, though, that might no longer be the case.
It really is! The more you read about it, the more interesting it gets, too - for example, while the virus is vertically transmitted, that doesn't happen by the ordinary route of mother-to-daughter infection. Instead, the viral genome is integrated into that of the wasp, as are genes that code for a unique type of ovarian cell that's specialized to act as a viral replicator.
And that's just one example! I could give more, like the effect the virus has on the wasp's reproductive host, and how it's honestly surprising that Peter Watts hasn't written a novel about that yet - I'm always happy to talk at length about wasps, or at least to whatever extent my interlocutor of the moment is happy to listen.
I can't see how that would possibly be a requirement for determining the species of a bee. Wouldn't DNA be cheaper and easier?