Yes, that’s what we did in our 2007 study - and lots of other similar studies have been done since. All of them support the conclusion that termites are cockroaches - or rather blattodeans (termites are still termites, but they are blattodeans, as are the ‘true’ cockroaches).

Interestingly (and significantly), the most ‘primitive’ termite, Mastotermes darwiniensis, produces an ootheca - see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1690738/

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Our 2007 paper did classify the termites as Termitidae, but we proposed a new and much better classification system in a slightly later paper i.e. Eggleton, P., Beccaloni, G. & Inward, D. 2007. Invited reply: Response to Lo et al. Biology Letters, 3(5): 564-565 (see https://www.researchgate.net/publication/262098913_E…