Probably less likely unless they are US based sites. These sites do remove files containing any notified copyright breaches. Sometimes this takes time but not usually more than a day or so. Of course if it is felt that some of these sorts of sites operating in the USA are even just initially distributing copyright material, or seemingly continuing to do so and hence contributing to online piracy, yes they might decide to block them 'just in case'.
It's the shades of 'just in case', or 'they might be' that is so unfair. The onus will be put (at whatever expense to them) - on the defending company or private individual to PROVE that they are not carrying out or assisting copyright breaches or online Piracy and this is where many serious troubles will arise, at least in the legal aspect of things, and the likelihood of an absolute plethora and torrent of lawsuits and defense cases. It's such a complicated legal situation that even the smallest cases will require hiring very expensive lawyers either by the litigating side if a defense suit is raised or those challenged with a takedown order. And takedown orders will be issued very routinely, immediately (and without question) on the copyright holders request without ANY reference to the courts or judiciary. (Yes, very big OUCH)
The big question re file upload sites utimately is whether your internet will be fast enough to download more than 2Mb in 2 days, if all external via the US routing is terminated if S.O.P.A. goes through (- as is completely expected to be the case with the internet and how it will have to operate in the aftermath of S.O.P.A.).
The worldwide DNS system excluding China depends on the integrity of the DNS IP address database. This would be entirely compromised by S.O.P.A., leaving no alternative but to remove all US IP address references (both personal and business) from the worldwide DNS database and to avoid routing any data packets or requests via any route which crosses or goes through the USA. The USA would have to negotiate links to and from the world wide web, and many very displeased non USA routing companies would either reject such requests or charge USA ISPs the earth for the facility. They could cap data transfers, severely limit transfer speeds and turn the facility off at a moment's notice making USA internet access outside of the USA, and our access to US websites as perilous and as difficult as reaching most Chinese websites.
If even more draconian action was taken under S.O.P.A. such as serving a multitude of takedown notices or even just serving aiding and abetting copyright breach notices on sites such as major search engines, USA internet access both outgoing and ingoing might be completely cut.
Also note that aside of trials for particularly heinous crimes, the number of likely defense suits in the courts would totally block up the entire US judicial system including the courts, for very many years to come for the foreseeable future.
There is also the aspect of right to invade ANYONE or ANY BUSINESS'S privacy by decrypting and inspecting data packets. This would reveal your browsing habits, private personal information and private communications, private and business financial information, secret business information and goodness knows what else to the authorities, government and judiciary. (Heaven help opposition politicians on this one).
We might all have to invent new forms of indecipherable language to communicate with any privacy on the net or by email or forums or live messaging. 'You hairy monkey have a tail up the mustang not we have over robo and them pirate flag' which loosely translates as 'we have a serious communication problem in getting anything around under S.O.P.A.! (or to the authorities it could mean the fast mustang isn't moving until the (dead-skulled) robo-like monkey gets its tail out of the mustang's butt!!)
S.O.P.A. is a complete and total menace to any not huge firm, to innovation, to the internet in particular, and to the US and Global economy, never-mind its completely nullifying effect on free speech, freedom of expression, freedom of ideas and human rights.
Anyone anywhere in the world's rights, privacy and means of communication will be severely affected and disrupted, not just by the precedent of S.O.P.A, but by the ongoing effects S.O.P.A. will have worldwide, economically, on the internet, socially and personally.