It depends....
for high frequency noise, the answer is an unqualified yes.
For low frequency noise, it is another issue.
I ignore the environment you'll be using your project or the required accuracy, so the following discussion may not be applicable or even required.....but for everyone's benefit, let's discuss it.
To have some decent attenuation, the corner frrequency has to be at least a decade below your offending noise. Powerline noise, which is ubiquitous, is 50 Hz, so the filter would have to have a corner frequency of 5 hz.
With a minimum 3 ohm, this boils down to aprox 10,000 microfarads.
To reduce the capacitor size, you can add some resistance in series with the Kelvin leads. Since the Picaxe's ADC requires a maximum series resistance of 10 kohm, the capacitor would now be reduced to about 3 microfarads. This may appear OK, but to reject common mode noise, the two sides have to be balanced with tight tolerance components. This requirement eliminates the use of electrolytic, tantalum and X7R or X5R ceramics. Essentially this will require the use of poly film caps, which are quite bulky and expensive.
On the other hand, an opamp has excellent rejection down to DC.
And a diff amp is fairly simple, as shown in the attached image. If you want unity gain, make all resistors equal. The only two caveats with this circuit is that it requires 1% or better resistors, and usage of a rail to rail amp, like the TLC2272 to tie the -Vcc supply voltage to ground (and avoid a negative supply).