Okay for races the PHB AD&D 1e introduced the traditional races that we think of as PHB races, the Human, Halfling, Dwarf, Elf, Half Elf, Gnome, and Half Orc. This provided those races a higher status over those only in supplemental books, more setting support, more of a presence in fiction and settings, etc...
While true, half-orc did not gain nearly as much cachet, despite being
well ahead of its time relative to other media. It wasn't until Warcraft came along that orcish PCs started to really gain traction. Likewise, it wasn't until Drizzt made a pathway for 99.95% of all drow to be brooding loners-with-a-posse rebels-against-evil that drow really got traction. Etc.
Usually, D&D races need an archetype first, before they really take off. Tieflings already had that archetype because "half-demon child" has tons of precedent across myth and folklore.
When 4e added Tieflings and Dragonborn their visiblitty in settings and stories just exploded?
Tieflings had been around well before that, and I don't really think 4e made them explode.
Dragonborn, on the other hand? Absolutely yes. They broke the mold--in part because, unlike pretty much every other similar thing, they
didn't have a particular literary or folkloric archetype to draw from. Yet they absolutely took off in popularity, and have if anything actually become
more popular in 5e (despite, ironically, being significantly
weaker, almost-inarguably the weakest PHB race.)
The main reason for this, I think, was that dragonborn tapped into something with inherent cool factor (dragons), and that 4e actually gave them a legitimately interesting and worthwhile backstory (scions of lost Arkhosia, carrying on a proud, noble, but also tragic legacy). Unlike most attempts at creating a new race, which just sort of give them a skirt-length presentation, dragonborn arrived with a fully-fledged
mythos to them, and it got more support with time.
Do you think the same will happen to the new races to the PHB?
From what I've heard, aardling is out, and the only "new" race is goliath. Giants are still cool, but perhaps not
as cool as dragons (don't @ me, I'm just commenting on general cultural cachet). Aasimar aren't new and I don't think adding them to the PHB will make any meaningful/long-term difference to them.
What do you think is the effect of a race getting added to the PHB?
It gives them prominence and legitimacy, but it doesn't guarantee that they stick in folks' minds. Gith, for example, have Dak'kon and now Lae'zel as poster characters, so if they were included in the 5.5e PHB,
that might be a combo that resulted in substantially increased attention. The question is whether that attention has staying power. Dragons will always be cool because they represent
power and
majesty, regardless of what culture you look at; it is inherently a subversion to make a weak or cutesy dragon. Gith may not be able to
sustain a PHB-driven boost, but certainly they'd get a boost, and probably never completely recede back to their old numbers, if they were added to the PHB.