It helps, though make sure that you've cooled it below 80F if it's a heated must. In practice, it takes a bloody lot of stirring/sloshing to dissolve much O2 into must. The strainer is an improvement... the goal is to get the most surface area of must into contact with air as possible, since air has less'n 20% O2 in it anyway it's a slow process. Serious geeks (and brewers, who boil the gasses out of their wort) use an aquarium pump with an inexpensive, sanitizable airstone on the end. These are great, and 10-15 mins will give a good charge of O2 to get going. Another hit at 12 hours is recommended for maximum yeast health (Drs. Fix and Fix, and Dr. Cone of Lallemand). Oxygenation is extremely important to let yeast build up strong cell walls, which is a huge factor in resisting alcohol to reach the published attenuation rate (and thus alcohol content).
Long and short of it, everything you can do to oxygenate is good until active fermentation is apparent, then knock it off.
I should add that there's a cool doodad called a degasser, basically a food-grade paint stirrer. It has two blades that fold up to go into a carboy, then flap out when it rotates. You just chuck it into a cordless drill (combining power tool use and meadmaking, ooh aah!), and fire it up. Dipping it in and out of the mead at speed will whip a lot of air in. Later on, stirring more gently with it will doslodge dissolved CO2 from the mead/wine, hence the "degasser". This'll give you a more still mead at bottling without the petillant sparkle that can otherwise persist, and permitting fewer oxidizing racking sessions to remove the CO2 and other gasses (hydrogen sulfide and, if you use sulfites, the sulfite gas).
Bees, brews and fun
in Lyons, CO