No, that's why the 80+ efficieny program exists.
One of the major requirements for an 80+ efficiency certification is for the PSU to have proper passive or active Power Factor Correction (PFC). If PSU is truly 80+ certified it should be at least 80% efficient at 20%, 50% and 100% of rated load with a true power factor of 0.9 or greater.
PSUs with active PFC are better and more efficient than passive PFC ones but they're the more expensive ones with high quality design and build. A PSU with passive PFC can reach 0.7–0.75 power factor and those with active PFC can reach up to 0.99 power factor.
Also note that even good efficieny PSUs with real gold and above certification are more efficient at 40-50% to 80-90% load. Except platinum ones are supposed to be 90% efficient from 20% to 100% and titanium units are supposed to be above 90% efficient from 10% to 100% load.
However, this is more relevant to your question, a PSU without any kind of power factor correction typcically has a power factor of only about 0.55–0.65. That is a 350W PSU (assuming it is of decent build - which is doubtful otherweise they'd apply for 80+ certification) can deliver clean and continuous 350W for a long time without overheating etc, will need to draw 538W to 636W AC (0.65 or 0.55 PF) from mains to deliver that 350W DC. Rest is dissipated as heat and electromagnetic into the air!
What is drawn from mains is almost twice what's delivered as DC at full load. If it has a say 0.72 PF (passive PFC) at 350W it only draws 486W. 636-486=150W. Every 6 and sth hours it draws 1 KWH more than a PSU with typical passive PFC. Depending on price of each KW and hours the PC is going to work say from 40% to 80% load that's some money in long term.
Regardless of all this, a PSU which is not good enough in design and build so the companies (OEM and the owner of the label/sticker rebranding it) couldn't even get efficiancy certification for it is not worth buying and using. What you have to keep in mind when buying PSUs (I think the most important component in every PC) is that such units, because of mediocre design, build and parts, are bad at voltage regulation, transient control, ripple suppression and these are harmful to other components. Also they're more prone to catastrophic failures in which they blow other components with them. They usually lack proper protection too.