This type of question has been addressed multiples times in RG.
The elastic modulus for metallic materials is dependent only on composition not the microstructure. If the composition remains the same whether it is friction stirred or fusion welded does not matter. If you can alter the bonding mechanism somehow for the same composition, say from metallic bonding to mixed type covalent-metallic, probably the elastic modulus may change.
the elastic modulus is dependent on temperature and composition of the material. So if you are testing the specimen in a constant temperature, the values should be the same. if you change the temperature, the bonding between atoms change and changes the elastic modulus.
Also, the microstructure in my opinion will change the elastic modulus. the modulus is stress/strain dependent and it will change if there is a stronger microstructure. for instance, in the case of steels, if you have martensite or austenite, the modulus will be different. so, I say yes to your question.