In principle you don't have to open all projects. However, when having updated a project and saving it you may be asked if you want to update other projects all well.

While setting-up your projects, however, it is essential that you have opened the pool first in order to use the external resources.

Why an easy solution if you can make it complicated?
Greetings from the Netherlands

I would highly recommend you prioritize said project tasks between these projects to prevent skewed resource planning. For example if you don't prioritize this relatively small resource pool you have for their project tasks, what can happen is you can very easily end up with a resource working on a different project every day which "usually" isn't the norm (key word "usually). I had one project whereby a resource changed tasks every other day, he finally shared with me that he works a project tasks at least for a solid week before moving to another project or project task on the same project. It made sense then that we prioritized all our project tasks.

Honestly after all that effort this particular group that works on console for NASA running live software for active missions (launch or station), they quit using the MS Project resource planning all-together because of the cumbersome administrative requirements. Personally I think it can be very helpful for very specific types of projects, but in my years of doing this have learned many PMs get excited about the "idea" of using resource mgmt, but stop when they first hand experience at least MS Projects software variation of resource mgmt. It's not too terrible to me, but many feel it's too labor intensive for at least smaller projects.

Hi Drew,

I understand that you are dealing with resource-constrained scheduling of multiple projects that share many common resources. When you want to move away from Excel for this kind of scheduling, do you consider MS Project as the best alternative? All popular project management tools are inefficient for resource leveling across multiple concurrent projects.

I can not agree that MS Project would not be capable of handling scheduling conflicts across several projects. When you want to apply levelling for over-allocated resources you can specify to do this minute by minute, hour by hour, day by day, week by week or month by month.
It is indeed possible to assign priorities to Projects. When levelling priority, standard the Project priority in first taken into account and only subsequently the priorities within projects for individual tasks. You can also level individual tasks manually.
I would anyhow always perform Levelling calculations Manual.
Realize that no levelling changes will be performed within the chosen time-frame. This as MS Project assumes that the resource would handle possible conflicts itself within the specified time-frame.
AS a general rule Task Duration should be in units of about the same length as your updates, including status dates settings, are apart. So, setting tasks as days, with many 1 or 2 days duration, is not realistic if you update only once a month.

Why an easy solution if you can make it complicated?
Greetings from the Netherlands