Depending on how long you plan on keeping the amp, buy the best capacitors you can justify putting into it. They will make a difference.
First: disregard zipost's rude comments. He's just grumpy because he only took second prize in the local village idiot competition. Hey zippy, better luck next time.
The Willsenton marked 0.33ufd cap is there to shunt any noise (high frequency crud) to ground. This is after the rectifying diodes where the AC is being converted to DC and any noise/hash not handled by the bigger cap is 'captured' by the small 0.33ufd and directed to ground, hopefully leaving the B+ supply in pristine condition. So to answer your fair question: Yes, it will most definitely effect the sound and the correct choice will do more than just improve tone. Think blacker background allowing more detail to be heard and all the benefits of that.
The purity of the power supply is paramount in any audio device as witnessed by the plethora of LPS units available to replace those cheap, small and generally noisy switching units. I have used a Mundorf Supreme (0.22ufd, think it was the Supreme) across the last cap in the PS with positive results. Do some research specifically on PS bypass caps.
Regarding the coupling caps: @charles1dad has some good advice. They will/can also have an effect on the end result. Duelund make a 0.01ufd cap for bypass duties and are very very good. In this coupling position you are preventing the HV DC from appearing on the output terminals and here you will find you can 'flavour' the sound. Ideally you are trying to 'do no harm' to your precious signal.
Miflex, Jupiter, Duelund, and many more to consider. The link to the cap shootout is a great guide.
Lots of good info already post. Parts are not that expensive so have at it. If it was me, I would use the V-Cap ODAM as my first choice and see if that floats your boat. We use them exclusively in our designs. We have also use the copper Milflex with good results. One of the best comments above is space. Be sure to look at the size specs first to make sure things fit in. Audio Note and Nichicon capacitors are excellent and so are the non-magnetic Audio Note resistors. Things get a little pricey but if you doing the labor that is a cost savings there. Last especially for tube equipment, look for AC filter chokes and other chokes to replace capacitors, etc. All parts have sound but to me, chokes are a big benefit plus a lot cheap!