Does GZIP Compression Level Have Any Impact On Decompression
Great question, and an underexposed issue. Your intuition is solid – for some compression algorithms, choosing the max level of compression can require more work from the decompressor when it's unpacked.
Luckily, that's not true for gzip – there's no extra overhead for the client/browser to decompress more heavily compressed gzip files (e.g. choosing 9 for compression instead of 6, assuming the standard zlib codebase that most servers use). The best measure for this is decompression rate, which for present purposes is in units of MB/sec, while also monitoring overhead like memory and CPU. Simply going by decompression time is no good because the file is smaller at higher compression settings, and we're not controlling for that factor if we're only using a stopwatch.
gzip decompression quickly gets asymptotic in terms of both time-to-decompress and memory usage once you get past level 6 compressed content. The time-to-decompress flatlines for levels 7, 8, and 9 in the test results linked by Marcus Müller, though that's coarse-grained data given in whole seconds.
You'll also notice in those results that the memory requirements for decompression are flat for all levels of compression at 0.1 MiB. That's almost unbelievable, just a degree of excellence in software that we rarely see. Mark Adler and colleagues deserve massive props for what they achieved. gzip is a very nice format.
The memory use gets at your question about overhead. There really is none. You don't gain much with level 9 in terms of browser decompression speed, but you don't lose anything.
Now, check out these test results for a bit more texture. You'll see how the gzip decompression rate is slightly faster with level 9 compressed content than with lower levels (at level 9, decomp rate is about 0.9% faster than at level 6, for example). That is interesting and surprising. I wouldn't expect the rate to increase. That was just one set of test results – it may not hold for other scenarios (and the difference is quite small in any case).
Parting note: Precompressing static files is a good idea, but I don't recommend gzip at level 9. You'll get smaller files than gzip-9 by instead using zopfli or libdeflate. Zopfli is a well-established gzip compressor from Google. libdeflate is new but quite excellent. In my testing it consistently beats gzip-9, but still trails zopfli. You can also use 7-Zip to create gzip files, and it will consistently beat gzip-9. (In the foregoing, gzip-9 refers to using the canonical gzip or zlib application that Apache and nginx use).
No, there is no downside on the decompression side when using the maximum compression level. In fact, there is a slight upside, in that better-compressed data decompresses faster. The reason is simply fewer compressed bits that the decompressor has to process.
Actually, in real world measurements a higher compression level yields lower decompression times (which might be primarily caused by the fact that you need to handle less permanent storage and less RAM access).
Since, actually, most things that happen at a client with the data are rather expensive compared to gunzipping, you shouldn't really care about that, at all.
Also be advised that for static assets that are images, usually huffman/zlib coding (PNG simply uses zlib!) is already applied, and you won't gain much by gzipping these. Actually, often small images (for example, icons) fit into a single TCP packet (ignoring the HTTP header, which sometimes is bigger than the image itself) and therefore you don't get any speed gain (but save money on transfer volume -- if you deliver terabytes of small images. Now, may I presume you're not Google itself...
Also, I'd like to point you to higher level optimization, like tools that can transform your javascript code into a compacter shape (eg. removing whitespace, renaming private variables from my_mother_really_likes_this_number_of_unicorns to m1); also, things like JQuery come in a "precompressed" form. The same exists for HTML. Doesn't make things easier to debug, but since you seem to be interested in ultimate space saving...