Tappets should not take long at all, but can take up to 15 minutes. I hardly doubt the oil pump has been affected but if in doubt, they are cheap enough to replace anyway, so you are doing the right thing.
To verify the oil pump, you could remove the oil filter and very gently cut it open near its base, making sure you do not drop any iron filings inside. Remove the element, cut it open and unfold it so that it looks like a consatina. Then inspect in th fold for metal or iron filings. if you see 'white' metal that is not affected by a maganet, then you have a bearing(s) that may have had something go through it. if you have lumps of ferrous metal, (iron, that is attracted to a magnet) or iron filings, then yes, you may have an oil pump issue.
If everything is ok, and you have a new pump and the tappetes are still noisy, then you can buy a new set of tappets quite reasonably from GSF. Bang these in and you should be sorted. I have GSF tappets in my G60 and they are perfectly ok.
