Yes, the blue colour may affect sleep cycles, but an app might not be enough to fix it, depending on other lighting conditions.
The existing answers are somewhat theoretical, without considering whether there is a pragmatic difference caused by real computer screens.
There has been a lot of research into the effect of blue light from computer screens and smart-phones and how they affect circadian rhythyms in humans.
Does screen light have any effect at all?
Twelve young adults were put in a dim room for four hours before bedtime, for five nights in a row. Each night, half read a printed book and half read from an eBook which emitted light.
We found that the use of these devices before bedtime prolongs the time it takes to fall asleep, delays the circadian clock, suppresses levels of the sleep-promoting hormone melatonin, reduces the amount and delays the timing of REM sleep, and reduces alertness the following morning. Use of light-emitting devices immediately before bedtime also increases alertness at that time, which may lead users to delay bedtime at home. Overall, we found that the use of portable light-emitting devices immediately before bedtime has biological effects that may perpetuate sleep deficiency and disrupt circadian rhythms, both of which can have adverse impacts on performance, health, and safety.
It is worth noting that a letter in response argued that the effect was confounded by the subjects not being exposed to normal light patterns during the day.
That is, the light emitted from the eReaders would have had a much smaller effect in alerting the brain than they would have had the participants been exposed to a normal pattern of everyday light exposure before using the eReaders before bedtime. Thus, the question still remains as to whether the light being emitted from an eReader, or any other type of electronic device, would actually impact nocturnal alertness and sleep in normally behaving individuals.
However, the original authors responded rejecting that their study had this shortcoming:
However, we disagree with the inference that the lighting conditions in our laboratory study overestimated the real-life effects of reading from a light-emitting eReader compared with reading from a printed book. First, participants in these studies were not “spending the entire day in dim room lighting.” [...] Second, such minor differences in daytime ambient lighting are unlikely to account for our findings.
(If it is easier reading, this study was discussed and put in context in this essay.
Is the Colour-Temperature Relevant?
In this study thirteen participants looked at iPad screens for a couple of hours under different conditions - just the screen (on full brightness), with additional blue leds shining on them, and with orange-tinted goggles that cut out the blue light. They had they melatonin-levels measured.
The present study extends results from Figueiro et al. (2011)
showing that a 2-h exposure to self-luminous tablets can result in a measurable, statistically reliable suppression of melatonin in Table 1.
That is, not wearing the orange goggles to cut out the blue light, lead to measurable changes in their melatonin levels, when viewing a regular iPad screen. Adding additional blue light increased the effect.
They add:
it is important to acknowledge that usage of self-luminous electronic devices before sleep may disrupt sleep even
if melatonin is not suppressed. Clearly, the tasks themselves may be
alerting or stressful stimuli that can lead to sleep disruption. For
now, however, it is recommended that these devices be dimmed at
night as much as possible in order to minimize melatonin
suppression, and that the duration of use be limited prior to
bedtimes.
What can be done?
This article takes a relatively theoretical approach, estimating the amount of different types of light that are produced by smartphone displays in typical use, and proposes some approaches to minimise the effects:
At night, if we use smartphone displays that are darker than that of the CIL threshold of light which activates circadian systems, the unhealthy effect of smartphone displays can be minimized.
It still requires further experimental support. However, they were able to highlight the limits of what can be achieved by adjusting the smartphone alone.
If we use smartphones at the proper distance and brightness setting in a dark room, the MSV can drop below ~1%. However, the use of a smartphone in a bright room at night significantly increases the [circadian illuminance] and MSV values [...] If people use smartphones in a bright room at night, it will be a little difficult to decrease the blue effect of smartphones on human health by varying smartphone variables that users can adjust. From the results of tuning the emitting wavelength of blue LEDs in a smartphone LCD backlight, fine control of blue light in smartphone displays can have a greater impact on reducing the unhealthy effect of blue light from smartphone displays at night. Thus, combating the unhealthy effect of blue light from smartphone displays at night does not simply mean turning off the smartphone, but rather using well designed [spectral power distribution] and the proper intensity of smartphone displays to see better where and when required while protecting people’s health and circadian rhythm.