Does standardisation restrain naturally occurring grammar change?

The answer by @user6726 is pretty much accurate. I'd just like to add a bit by challenging the assumption that the processes of standard maintenance (dictionary writing, usage guides, schooling, public discussion, etc.) are in some way in opposition to 'natural' language change. That is exactly how language change occurs. The normative standard is just one of the dialects with higher prestige in certain contexts and therefore higher motivation for emulation. However, that prestige may wane with time (as happened in the UK) and various challenges will appear to undermine some aspects of the standard - this will include pronunciation, morphology, syntax and vocabulary. For instance, English has seen the spread of [be+Ving] construction to more and more verbs to expressions such as 'I'm liking this more and more'.

Also, the processes of standardization did not just appear in 19th century. They were always around but in different forms.

The question is did things like mass education and mass media slow down change or slow down change in some areas? This is a question that's difficult to answer because no one knows what the rate of language change should be over relatively short periods of time like 200 years. Some languages change a lot in that time and others remain relatively stable. We know that things like increased contact and social change have an impact but even that is not predictable. RMW Dixon proposed punctuated equilibria as the answer to the question but I'm not aware of any research that followed up on it.