One of the members of my local business group asked me just that recently. The answer is usually yes. When you go into your dashboard, if an update for WordPress is available, there will be a yellow bar across the top of the screen inviting you to update. There are also black circles in the dashboard telling you how many updates are available for your site.
Before updating, it’s always a good idea to back-up your site. Go to ‘Tools’ in the dashboard and select ‘Export’.
Click the ‘Download Export File’ with ‘All content’ selected, then do the same again with just ‘Posts’ selected to make a back-up of your site, should your developer need it.
Select the ‘Updates’ link from your dashboard which will bring up a screen like this:
Update WordPress first. If you are using a WordPress theme or a child theme, update those themes next. If you are using a custom theme, the option to update that will not appear (as it doesn’t need to be updated). If you have an ‘adapted’ theme, you are on shaky ground, as updating that will wipe-out any customisation.
It’s safest to wait a couple of weeks before you update your plug-ins. You may have happened to log into your site just as the new version of WordPress has been launched. If this is the case, there may be some glitches that the plug-in developer needs to sort out.
Every time you update, there is a very small chance that some elements of your site may become incompatible and things do not work properly; this is the time to contact your developer. However, if you don’t update, you run the risk of your site getting hacked.