The overwhelming opinion of demographers and those who study these matters seems to be that there will be a baby bust in most developed countries (and probably across some of the less developed world as well, though some poor countries may see upticks in births).
There will be a small number of contraceptive accidents and people who were planning a baby anyway and decided to bring it forward because "This year and the year after are going to be rubbish for careers, eating out, travel and social life---why not do the baby stuff right now?"
However, all in all births will almost certainly fall. Due to:
Worries about getting the virus while pregnant
Worries about birth and the baby experience being bloody miserable due to all the rules
Lockdown stress
Severe economic uncertainties (and I mean severe---we are staring down the barrel of a massive recession right now)
General drumbeat of doom (if pandemics are possible, what's the next black swan going to be? War with China? Mass power outages? Supervolcano eruption? God knows what?)
General sense that families with young kids seem to be at the bottom of the priority pile right now. Even that stupid NHS clapping thing---timed right for the toddler's bedtime, fucking brilliant idea. After parents have been going out of their mind trying to WFH while said toddler trashes the place and launches themselves off the furniture. A little thing, but just so symptomatic of the way exhausted parents have been treated throughout this nightmare.
Looking at the historical perspective, disasters and pandemics nearly always result in a fall in the birthrate and fertility rate, contrary to what some people like to believe. The post-WWII baby boom was highly unusual, and was caused by a set of very particular factors which are not in place right now. The financial crisis of 2008 is a better analogy, frankly. From 2010 onwards, the fertility rate in most countries started dropping fast and actually never recovered (= as soon as the real-world consequences of the crash started to be felt, people started planning fewer pregnancies). We will probably see something similar after this.
Some individual hospitals have been excitedly reporting "baby booms" but this is almost certainly misleading. COVID-related factors-the fact that some hospitals may have reduced maternity coverage, or had restrictions in place which were particularly unappealing to families, or became known as COVID hotspotswill have caused some families to switch towards certain hospitals in preference to others. So some individual hospitals will have noted increases in births, but this is not the same as an overall baby boom.