Depends on the quality of the PSU you've got. If it's cheap and it's trying to supply too much power it might work for a while, then overheat/overload, fail and destroy your whole system.
If it's good quality then it MIGHT just drop out when too much power is drawn from it. Sometimes your system will just power off or the GPU might just turn off when booting up. Like when the CPU is too hot it just shuts down.
If it was me and I had a 400W PSU and my BRAND NEW Graphics card manual said I needed 550W min. I wouldn't risk using a low powered PSU and possibly wreck everything. But I am paranoid. You on the other hand might be a carefree spirit and believe everything will be okay.
400 isn't enough in my eyes.
The person that told you it
"cant do its maximum effect" is misinformed. What do they think? It can only max out to 2xAA or something when it hasn't got enough juice? It's not a light bulb.