Immortal Procreation Clause: Somewhat played straight, but only somewhat. Eldraeic native fertility is considerably, about an order of magnitude, lower than human as a baseline, yes, but that’s not so much lower that they weren’t running a nice healthy population growth curve before discovering technology, space, etc. (and started on a large and very sparsely populated world), and even post-that with the normally-ensuing technical-society decline, the trend is still upwards on net. Fortunately, there’s any amount of space in space, and simply oodles of unused resources, too.
(Demographically, it’s low enough to make non-adults very much the minority in the population – certainly enough that an attempt at, say, mass schooling on our model, were that particular form of collective madness to set in, would require very large catchment areas indeed – and to, economically, put a healthy premium on the cost of labor and encourage capital-intensive models right from the start, but certainly not low enough to produce dwindling-elvish-dying-race effects, even with non-natural deaths included, or anything like that.)
In a more general case, immortagens typically do not affect fertility one way or the other. Sensible species are expected to learn how to manage their own birthrate. Insensible species needn’t come complaining when they have an overpopulation crash because this bit of data is right there on the tin, look. (Insensible and warlike species may discover that having your population managed for you is also an option. If not a good one.)