I thought I heard somewhere that you shouldn't enter until level 23. I think it was due to some leveled items. Is there any reason for concern, and does the quest award leveler made by the 2 guys who made the unofficial patches cover it?

no, loot and enemies are scaled to your level.

Quest Award Leveler supports SI, so you're free to head in whenever you please.

it decides the loot on your level, if it's a quest reward then it depends what level you are at a certain point in the related quest.

When you hear 'level 23' in conjunction with SI, people are referring to obtaining the top levels of Amber or Madness equipment. No reason to wait for this. This gear is unique in that you can have new sets made whenever you want and it's level will be set to when you have it made. No worries there.

Leveled quest reward items are another matter. The level of those are permanently set to your level when you complete the associated quest. Some of the top leveled quest reward items for SI are available at level 25, others at level 30.

My recommendation? Enter when you want and have fun. Check UESP wiki if you want and check out the leveled quest items for SI. If you absolutely, positively gots to have one or more of them at top level, simply delay the asssociated quest until you are at the required level.