That depends upon just how good the DAC in the CD player is. If it's a newer high-end CD player, perhaps it's DAC is better and you could use the analog outputs. I have a 15 year old Sony CD 5-disk changer so I link with digital optical TosLink to my NAD T758, as the receiver's DAC is newer and better. Since I got a Bluesound Vault and ripped all my CD's to it, the Sony CD changer collects dust.
As for phono amp in the C338 or C368, it's pretty good. How much better is a good Conrad Johnson, Bellari, or host of others, I don't know. Your TT and cartridge may be more of the limiting factor. Consider the BlueOS module in the future because your integrated amp can become a super tuner playing radio stations from nearby...or anywhere in the world. Even if you never subscribe to a streaming service such as Tidal Hi-Fi (very highly recommended as it now has MQA encoded titles and BlueOS decodes them), you'd still be able to play every CD you own if you simply rip them to a network attached storage drive.
For far less than the cost of a good CD player, BlueOS gets you incredible possibilities. You only can add that to the C368 or C388 though. A C338 would need to use a Bluesound Node. The original ones are on closeout right now for about $300. A Node 2 runs $449, so you see why adding the module to your integrated amp makes sense.
KEF R500, R200C, R100, SVS SB2000 sub, NAD T758 receiver, Pro-Ject RPM1 TT w/ Ortofon 2M Red, Bluesound Vault2, Sony BDP-S480 BlueRay player, Samsung UN55JU6500F 4K LED TV, KEF M500 headphones, Sony CDP-CE500 CD changer.