You can install as much physical RAM as your hardware supports without any performance penalty on 32-bit Windows. The only catch is a 32-bit OS will ignore all but ~3.5 GB due to the limitations of using 32-bit memory addresses.
Now, it is possible to use more than ~3.5 GB of RAM on a 32-bit OS. However, this introduces a performance penalty because the 32-bit OS must use extra processing to overcome the 32-bit limitations. This is not the default setting for most versions of 32-bit Windows (only server versions even have the ability.) Linux may default to trying to use as much hardware RAM as possible.
In your specific case, I would be more worried about making sure the new stick of RAM matches the old stick. If they do not match, there may be a performance hit in order to allow the RAM to work together. And of course, introducing bad RAM will affect the stability of your system.
Update: that extra stick of RAM will require additional electricity, so performance in terms of battery life may be reduced. However, it may not be significant because the display, CPU, GPU, and hard drive are the main consumers of battery power.
Longer explanation of the 32-bit addressing limitation:
In order to do basic operations on memory (read and write), the OS needs a method to select
which part of memory will receive the read or write. For efficiency, 32-bit OS's use 32-bit addresses. Since each address holds 32 bits of data, up to 4 GB of memory can be addressed.
If the OS used this 32-bit address to access only RAM, exactly 4 GB of RAM could be used. However, there are special areas of this address space that are used for other purposes. Usually the biggest special area is video memory from the graphics card.
Now, to overcome the 32-bit addressing limitation (on a 32-bit OS) an offset is also added to the addressing scheme. This is the source of the performance penalty. Instead of using a simple 32-bit memory address directly, an extra offset value must also be checked.
Even more detailed explanation.