The short answer is yes. However this is not recommended.
The probes have a list of preprogrammed standard options which have a built in non-linear temperature correction curve specific to each standard. It is recommended to calibrate with the standard from this list that is closest to the conductivity of the samples to be tested. The standard used in the calibration can be changed by selecting the Wrench button > CDC401 settings > Modify current settings > Calibration options > Standard. Below is the list of preprogrammed standards to select from.
• 1 D KCl, 111.3 mS/cm, 25 °C
• 0.1 D KCl, 12.85 mS/cm, 25 °C
• 0.01 D KCl, 1408 μS/cm, 25 °C
• 0.1 M KCl, 12.88 mS/cm, 25 °C
• 0.01 M KCl, 1413 μS/cm, 25 °C
• 0.001 M KCl, 146.93 μS/cm, 25 °C
• NaCl, 18 mS/cm, 25 °C
• NaCl, 1000 μS/cm, 25 °C
• NaCl, 25 μS/cm, 25 °C
• NaCl, 0.05%, 1015 μS/cm, 25 °C
• Seawater (S=35)
"Custom" is an option in this list as well. If custom is selected this opens up four additional options in the calibration options menu.
• Standard Unit (either µS/cm or mS/cm)
• Standard Value
• Reference temperature (almost always going to be 25 °C)
• Temperature correction
The temperature correction option is the reason that custom standards are not recommended. By definition the conductivity of the standard will be equal to the Standard value at the reference temperature but not at any other temperature. At a full temperature range this relationship between the difference in measured temperature and reference temperature verses the difference between the measured conductivity of the standard and the standard value (at the reference temperature) is non-linear. Within a smaller temperature range, a linear regression (using a temperature correction factor) of this relationship can be assumed, but will be less accurate than non-linear curve. The accuracy of a linear correction relative to a non-linear correction decreases the further from the reference temperature the measured temperature is. See also:
What's the difference between temperature compensation and temperature correction? (pH verses Conductivity temperature adjustments)
If a custom standard is used, it would require the use of a linear temperature correction factor (in %/°C) to be used. The factor is adjustable and would need to be changed to reflect the relationship between temperature and conductivity specific to the standard being used in the temperature range that the standard will be in during the calibration. If the standard is always at 25 °C this would not be an issue, but this cannot be guaranteed and is often not the case. The linear correction factor is often unknown, and would need to be determined by the end user before calibration with the standard can be performed. This is time consuming, difficult, requires additional instrumentation. Even if a good correction factor is identified, it will never be as accurate as a non-linear correction curve. This is why it's recommended to use one of the preset standards instead of a custom standard.