If you are thinking of a particular chip, you should mention it.
Generally, full speed USB requires a timing accuracy of +/- 0.25%. Most internal oscillators are never able to keep it.
FTDI FT232R is one of the few chips that do full speed USB with an internal oscillator.
The said Cypress controllers are low speed USB. Also other vendors USB processors (e.g. from Microchip) are
able to achieve 1.5% low speed accuracy with an internal oscillator The enCoReIII full speed controller is said
to achieve 0.25% accuracy by self-tuning a low accuracy internal oscillator to the USB.