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No it won't. US for European servers is no problem, round trip of <200ms is hardly noticeable (unless you have a lot of round trips and no CDN). It appears that Google looks at render times (at least that's what they communicate) and it's easy to lose 200ms by having 5 js resources even if the server is close. But Asian visitors will notice a deterioration if you had a server in US-West before. Latency Europe-East Asia/Australia is very high.

SEO is a black box, so there are no definite answers. It will affect load times (the 60ms) and that could have an effect on search engines.

Highly doubt Google and others would punish you for having a slightly bigger latency to your server and back.

If that was the case, all the companies that are hosted in the US would already be punished in Europe.

Keep the response form Apache as small as possible and put static content in a CDN. Your SEO shouldn't be affected by that.

That said, noone knows the rules for Googles Ranking algorithm, so I guess you will have to try.