No. There is enough apps what I start, use and close. Why it should check the update every time it starts?
And this is even more irritating when the update check isn't working for some reason, eg update URI is not available but overall Internet works, now you sit there and wait while the update checker timeouts. Why, why?
Sounds like a decision that could only be made by a company that believes their API will change often (or is for whatever reason worried about 0Ds) and without enough engineering headroom to handle versioning and translation layers correctly. It could greatly simplify a style of development that allows companies to move quickly without paying certain costs.
At startup is perfectly fine. Then once every 24 hours later if the app hasn't exited is also perfectly fine.
More often than that is too often. Every 5 minutes? That's ridiculous.