Unpickled StringArray with pd.NA raises ValueError
#### Code Sample, a copy-pastable example if possible

```python
import pandas as pd
import pickle
df = pd.Series(['abc'] +  [pd.NA]*60, dtype='string')
serialized = pickle.dumps(df)
unserialized = pickle.loads(serialized)
print(unserialized)
```
#### Problem description
The unserialized df cannot be printed. Fails with
ValueError: StringArray requires a sequence of strings or pandas.NA

Note that things work fine with less than 60 pd.NA
```python
import pandas as pd
import pickle
df = pd.Series(['abc'] +  [pd.NA]*59, dtype='string')
serialized = pickle.dumps(df)
unserialized = pickle.loads(serialized)
print(unserialized)
```


#### Expected Output
Print out simple df 


#### Output of ``pd.show_versions()``

<details>

INSTALLED VERSIONS
------------------
commit           : None
python           : 3.6.7.final.0
python-bits      : 64
OS               : Linux
OS-release       : 3.10.0-1062.9.1.el7.x86_64
machine          : x86_64
processor        : 
byteorder        : little
LC_ALL           : C
LANG             : en_US.UTF-8A
LOCALE           : None.None

pandas           : 1.0.0
numpy            : 1.18.1
pytz             : 2019.3
dateutil         : 2.8.1
pip              : 20.0.2
setuptools       : 45.2.0.post20200209
Cython           : 0.29.15
pytest           : 5.3.5
hypothesis       : None
sphinx           : 2.4.1
blosc            : None
feather          : None
xlsxwriter       : 1.2.7
lxml.etree       : 4.5.0
html5lib         : None
pymysql          : None
psycopg2         : None
jinja2           : 2.11.1
IPython          : 7.12.0
pandas_datareader: None
bs4              : None
bottleneck       : None
fastparquet      : None
gcsfs            : None
lxml.etree       : 4.5.0
matplotlib       : 3.1.3
numexpr          : 2.7.1
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : 0.16.0
pytables         : None
pytest           : 5.3.5
pyxlsb           : None
s3fs             : None
scipy            : 1.4.1
sqlalchemy       : 1.3.13
tables           : 3.6.1
tabulate         : None
xarray           : 0.15.0
xlrd             : 1.2.0
xlwt             : 1.3.0
xlsxwriter       : 1.2.7
numba            : 0.48.0

</details>
