Problems you may face:
1. It isn't temperature stabilized so expect some frequency drift as it warms or cools.
2. It isn't voltage stabilized, frequency will drift as the battery discharges.
3. The proximity of items near to the antenna will shift it's frequency.
4. Both sides of the tuning capacitor are 'live', expect the frequency to shift as you touch the control as well as turn it.
5. The modulation control is poorly wired and will only have limited range.
6. For most electret microphones (a true condenser mic would not work in this circuit) the value of R9 is too low, a value between 4.7K and 10K would be more appropriate.
7. Some of the other values are not optimal.
Having said all that, it might work. If it doesn't, try connecting a capacitor of 10nF from the top of C3/L1 to ground.
Brian.