In ASTM's Standard for Acrylic Dispersion Grounds (ASTM D 7733) three coats of a good quality acrylic ground (aka acrylic gesso) should be sufficient to block oil penetration. We happened to be the lead chair for the development of that standard and so became intimately involved in the testing and evaluation it was based on. And in fact the vast majority of good quality acrylic gessoes did meet that requirement, which should give you some comfort. That said, however, without actually testing your specific product, it is hard to know if it absolutely meets that standard. We will give some hints on how to test below.
We would also point out that since three coats of a high quality acrylic gesso should block oil penetration on their own, a size is not 100% necessary. The acrylic grounds can really serve both functions. Where a size is absolutely critical and necessary is whenever an oil ground is being applied directly to to a canvas.
Also, one question we would ask right off the bat is simply have you seen any strikethrough on any of the canvases you have done? If not, then you should have nothing to worry about. Some people get concerned that it will appear later on, but in truth if strike through happens it will be apparent during the drying process. So, if so far all looks good, I would rest easy.
That said, if you want to test this brand of canvas and have one to spare, there are two types of tests we would recommend. One, which is really a worse case scenario test, requires that the canvas be absolutely level, then apply three drops of linseed oil from a pipette or medicinal dropper and let that sit there and dry for a couple of weeks. During that time it should spread out and penetrate into the ground slightly - showing the ground in absorbent enough to provide good anchoring - but it should NOT penetrate through. On the other hand, it also should not stay put and dry as a raised bead where no penetration or spread is apparent. That is also a failure.
An alternative, and more of a real world test, would be to apply whatever is the thickest application you would conceivably do, using a slow-drying high oil content paint. Alizarin crimson is perfect for this (perhaps the one use of it that is beneficial!) or an organic red, like a quinacridone or napthol red, and let that dry and see if oil penetrates through. You can also try applying some of these colors with some additional medium or some solvent, to see if in a glaze or a wash anything penetrates. Again, if the back of the canvas stays nice and clean, then no worries.
If after all of this you are still concerned, or if your tests show any failures, then yes - applying additional coats of a high quality acrylic gesso will help. And some artists will do that regardless simply because they like the convenience of a pre-stretched canvas but like also having control and knowledge of the specific ground they are painting on. Also, it can help standardize the feel of the surface regardless of the brand of pre-stretched canvas you use.
Hope the above is helpful. And to summarize, three coats of a good quality acrylic gesso should block any oil penetration and in the testing for the ASTM Standard most good quality ones had no problems passing that requirement.
Senior Technical Specialist
Golden Artist Colors