Quick question - is there anything in particular to take into consideration when upgrading Drupal, if it is used as a platform for CiviCRM?
Or can I just go ahead with Drupal update as if there was not CiviCRM installed?
It depends on the upgrade i.e from 6.x to 7.x to 8.x. If its a simple and internal version i.e 7.12 to 7.29 than you can perform update directly and you won't have problem in CiviCRM but if its from 6 to 7/8 then you will need to replace the CiviCRM files with same version for D7 or D8 and then clear CiviCRM cache(probably delete template_c).
Note: Backup Database and filesystem before performing upgrade.