Definitely test for conversion. This is a key test when you are starting out or trying new recipes. You will most likely have no problems unless your water is unusual or you are brewing very pale or very dark beers but if you do run into problems knowing whether you had complete conversion or not will help you troubleshoot. If conversion is incomplete after your mash you can let it go longer but the enzymes are denaturing over time so the rate of conversion is continually slowing down.
Some pointers on doing the test. You only need a drop of fluid from your mash. Try not to get grains or much debris in it. Place it on a white background and add a drop of iodine to it and swirl it around. Starch will turn dark purple/black. There will always be some starch granules and small grain debris that will turn black. What you are interested in however is the liquid portion with the dissolved starch which should turn the same color as the iodine you added. The first few times you do it start checking right at the beginning of your mash and then every time you stir it, this will help you distinguish the solution change from the always present undissolved starch. At the same time taste the fluid, it will become noticeably sweeter as the mash proceeds!