As said in another answer, this episode does not occur in Sri Valmiki Ramayana but in Sri Ramacharitmanas of Gosvami Tulasidas.
Following is the original text with hindi translations from Gita-press gorakhpur's edition (english translations are mine) from LankA-KAnda which contains this episode:
जौं मम चरन सकसि सठ टारी । फिरहिं रामु सीता मैं हारी ।।
अरे मूर्ख! यदि तू मेरा चरण हटा सके तो श्रीरामजी लौट जायँगे, मैं सीताजीको हार गया।
Angad said: If you can move my leg than Lord Shri Rama would go back without >Shrimati Sitadevi and we would lose.
सुनहु सुभट सब कह दससीसा । पद गहि धरनि पछारहु कीसा ।।
रावणने कहा—हे सब वीरो! सुनो, पैर पकड़कर बंदरको पृथ्वीपर पछाड़ दो ।।५।|
Ravana said: Listen everyone! Knock down this monkey by pulling his leg!
कपि बल देखि सकल हियँ हारे । उठा आपु कपि कें परचारे ।।
अङ्गदका बल देखकर सब हृदयमें हार गये। तब अङ्गदके ललकारनेपर रावण स्वयं उठा।
Seeing Angad's strength everybody accepted defeat. And then being challenged by Angad, Ravana himself got up.
Here the word used is परचारे (parchAre) which would mean that Angad challenged or shouted Ravana to come
गहत चरन कह बालिकुमारा । मम पद गहें न तोर उबारा ।।
जब वह अङ्गदका चरण पकड़ने लगा, तब बालिकुमार अङ्गदने कहा—मेरा चरण पकड़नेसे तेरा बचाव नहीं होगा! ।।१।।
When he started holding Angad's feet, Angad said: you won't be saved by holding onto my leg. :-)
There is no where mentioned that Angad removed his feet, but instead he humiliated Ravana
गहसि न राम चरन सठ जाई । सुनत फिरा मन अति सकुचाई ।।
भयउ तेजहत श्री सब गई । मध्य दिवस जिमि ससि सोहई ।।
अरे मूर्ख! तू जाकर श्रीरामजीके चरण क्यों नहीं पकड़ता? यह सुनकर वह मनमें बहुत ही सकुचाकर लौट गया।
उसकी सारी श्री जाती रही। वह ऐसा तेजहीन हो गया जैसे मध्याह्नमें चन्द्रमा दिखायी देता है ।।२।।
Why don't you hold on to Lord Shri Rama's feet? Listening to this Ravana was very embarassed.
He became bereft of all lustre just like moon loses its lustre at mid-day.
सिंघासन बैठेउ सिर नाई । मानहुँ संपति सकल गँवाई ।।
जगदातमा प्रानपति रामा । तासु बिमुख किमि लह बिश्रामा ।।
वह सिर नीचा करके सिंहासनपर जा बैठा। मानो सारी सम्पत्ति गँवाकर बैठा हो।
श्रीरामचन्द्रजी जगत्भरके आत्मा और प्राणोंके स्वामी हैं। उनसे विमुख रहनेवाला शान्ति कैसे पा सकता है? ।।३।।
With head hung low he went and sat on his throne as if he has lost all his wealth.
So here it seems, Ravana didn't even tried lifting Angad's legs but was humiliated that a King of his stature is stooping low to touch the feet of just an insignificant servant of Lord Sri Rama, so what will happen when Lord Sri Rama himself arrives!
Lord Shri Ramachandra is the soul of the world and master of all living beings, how can one be peaceful without being friendly towards him?
उमा राम की भृकुटि बिलासा । होइ बिस्व पुनि पावइ नासा ।।
तृन ते कुलिस कुलिस तृन करई । तासु दूत पन कहु किमि टरई ।।
[शिवजी कहते हैं—] हे उमा! जिन श्रीरामचन्द्रजीके भ्रूविलास (भौंहके इशारे) - से विश्व उत्पन्न होता है और फिर नाशको प्राप्त होता है;
Oh Uma! Just by the movement of the eyebrows of Lord Shri Ramachandra this whole universe is created and destroyed;
जो तृणको वज्र और वज्रको तृण बना देते हैं (अत्यन्त निर्बलको महान् प्रबल और महान् प्रबलको अत्यन्त निर्बल कर देते हैं), उनके दूतका प्रण, कहो, कैसे टल सकता है? ।।४।।
That Lord Sri Rama who can make the weak very strong and the strong very weak, how then can his servant's/messenger's vow be nullified?
Here it explains clearly that one who is a servant of Lord Shri Rama how can his vow be nullified that simply means even if Ravana would have tried it Angad's feet would not have budged
जातुधान अंगद पन देखी । भय ब्याकुल सब भए बिसेषी ।।
अंगदका प्रण [सफल] देखकर सब राक्षस भयसे अत्यन्त ही व्याकुल हो गये ।।७।।
All the Rakshasas became very fearful seeing that Angad's Vow was successful.
So at the end we see that its clearly written that Angad's vow ( पन / praN) was successful.
So to answer your first question:
No Ravana couldn't have moved it even if he would have tried.
To answer your second question whether we can understand anything else from this episode?
One thing i can understand is that how a servant should do service to his master. Angad like Hanuman did more than what was expected of him, one he tossed Ravana's helmet (in previous verses 6.31 to 6.33) to Ram's feet, he humiliated all of the Rakshasas including Ravana which is very important in a battle i.e. to lower the morale of the opponent.
Another thing we can learn is he showed that he has full faith in Lord Shri Rama and hence he had the strength to be bold enough in front of all the Rakshasas and that is why nobody could even move him.
Another thing is that a servant should never hear blaspheme of his master, if he has to hear, he should behave just like Angad and make the blasphemer pay for their impudence and thus silence their blasphemy. :-)