Is this a theoretical question or a practical questions?
In theory, yes you want good speaker for your surround speakers.
But practically, it is your circumstances that determine which Surround speaker will work in your situation. In some case, bookshelf are impossible, so you go with Lifestyle Satellite speakers. In other case, in a large dedicated room, the Surround could be floorstanding speakers.
I can hear a real and very significant difference between my $150/pr bookshelf speakers, and some $250/pr bookshelf speakers I recently tried out. So, yes there is a threshold where sound improves dramatically.
Next, how will the system be used? If this is a Movie only system, Surround can be smaller and less full range within reason. If you like Multi-Channel Music, or if you listen to music in All-Channel Stereo, then perhaps more emphasis could be placed on the Surrounds.
Next, Budget, yes you can spend THOUSANDS on Surround Speakers, but ...do you have thousands to spend? If not, then we have to work on something consistent with your budget, and in balance with the rest of your equipment.
So, I would say, within the context of working budget and the other equipment, that there is something of a minimum standard for Surround Speakers, but that minimum standard is not quite as high as it is for Front and Center speakers.
You don't want crap Surrounds, but anything of a fair and reasonable standard of good, is going to be fine.
To accurately answer the question it needs some real world context. If you have a Home Theater in a Box from Walmart, then what you have for Surrounds won't matter much. On the other hand if you have a $15,000 Home Theater system, then you probably want to spend a bit on the Surrounds. If you have a $2000 to $5000 Home Theater system, which the Surrounds won't remotely cost as much as the Front speakers, they should be more than Walmart crap.
As a generalization, yes, the Surrounds do matter, but without the context of the details of the Room and the Specific System that the Surround will be paired with, it is difficult to make any definitive statements. I think Surrounds in reasonable balance with the rest of your equipment, consistent with our budget, and appropriate for the specific room are the factors that make the decision.
But then ... that's just my opinion.
Steve/bluewizard