Short answer: Maybe
Here is why: The cable may be rated for 300 volts but it is not #14 gauge minimum size for power and lighting as stated here:
(A) Minimum Size of Conductors. The minimum size of conductors shall be as shown in Table 310.106(A), except as permitted elsewhere in this Code
Table 310.106(A) shows the minimum size to be #14 gauge wire.
However, if you get a 7 amp breaker or fuse marked for use with #18 ga wire or a special class of fuse, you could use this section
Article 240.4(D)(1) 18 AWG Copper. 7 amperes, provided all the following conditions are met:
(1) Continuous loads do not exceed 5.6 amperes. (2) Overcurrent protection is provided by one of the following: a. Branch-circuit-rated circuit breakers listed and marked for use with 18 AWG copper wire b. Branch-circuit-rated fuses listed and marked for use with 18 AWG copper wire c. Class CC, Class J, or Class T fuses
This would be very strange in a house though so your inspector may not want to allow it.