NO. Please understand. There won't be any problem. However you cannot play modern games at low/medium settings with that card at default clock speed, you can just overclock it from catalyst control center. It will work just fine. For example, I have a legacy computer with this configuration:
CPU: Pentium 4 511 2.8GHz
GPU: Sapphire Radeon HD 5450 2GB
RAM: 2GB DDR1
HDD: 80 GB (ATA)
It still runs Half Life 2 Episode 2 on ultra settings at 1152 x 864 resolution with full AA and full AF. So, you see, some GPU intensive games can run on this card well - provided that you can increase the clock and memory frequency a bit. Another example, NFS Most Wanted (2005). It runs smoothly on 1024 x 768 with all settings on high and 0xAA (my CPU is a bottleneck).
Don't think that I'm quoting only old games. I just want to say that you can get that kind of a quality on this card. Otherwise, reduce the graphic settings, install the correct drivers and make sure that you have enough ventilation in your case so that your card doesn't heat up much.
*Can you tell me what your RAM and mobo is? I can suggest some games.*
That should help.