Is laminating the planks enough to counter the tendency to warp that plainsawn lumber
Basically yes although there are no guarantees.
'Jointed' slabs are inherently stable, even when one or more of the individual boards are less than ideal, because of the construction.
The long-grain glued faces are immensely strong and individually and together will work to keep the glue-up flat. And a rough rule of thumb is that the more glue joints there are the stronger the piece ends up. But for wide projects the more joints the more difficult the glue-up becomes, so it can be advisable to do it in sub-assemblies and then glueing these together to make up your final width.
For maximum stability be aware of the radial and tangential direction of the grain and try to orient this uniformly for every piece. This is not always possible but it's a good thing to aim for as the more uniform you can make the seasonal expansion and contraction the better.
The ideal is to orient the tangential grain such that the greatest expected movement is up and down, not side to side. Side note: this is one reason for the traditional preference for quarter-sawn wood, which tends to expand less across its width than plain-sawn or flat-sawn boards.
I'm concerned because of the poor quality of dimensional lumber.
Stock selection is often overlooked today but it's perhaps more important now than ever, especially with dimensional lumber which can be of poor uniformity, and is outright poor quality at times.
The best course would be to select your two-bys for straight grain and being free from knots and defects over a number of visits but again this is not always possible, given individual circumstances and sources of supply.