In fact, at 1,691 hours per annum in 2015, Spain is slightly below the median of 1,749 and mean of 1,756.
Spain does not have longer working hours in comparison with other OECD countries
Long hours reduces birth rates
Lack of correlation is strong evidence of lack of causation. Using the data above (averaged in 5 year blocks between 2000 and 2015) and cross referenced with UN data on crude birth rates gives:
(The graph is produced by averaging the hours worked from the OECD data set ito 2000-2005, 2005-2010 & 2010-2015 blocks to correspond with the UN data points, matching the data for each country and plotting as an x-Y scatter).
There is a correlation, however, it is tiny (R2 = 0.1) and it is obvious from the look of the graph that there is a lot more noise than signal here. Notwithstanding, it goes the wrong way, that is, longer hours are correlated with higher birth rates.
A reduction in hours worked is not correlated with higher birth rates
Firstly we see that the average time for intercourse is roughly similar to other European countries (France aside). So Spanish couples aren't taking less time in having sex.
However we see that the satisfaction in women is markedly different:
Spain standing out within Europe as giving less attention to women for them achieve orgasm. Given that women take longer to orgasm we could interpret this as that, on average, less time was put aside for foreplay.
As you can see I've proven nothing: however from another perspective to the research provided the hypothesis was supported.
Also I couldn't find the numbers used to provide these graphs - those would probably provide a better insight into the differences.